Simplify: $\frac{3a^2\;-48}{48\;-24a + 3a^2}$

Simplify: $\frac{3a^2\;-48}{48\;-24a + 3a^2}$

Answers

Factorise numerator

3a² - 24a + 48

P = 144; S = -24; N = -12, -12

(3a² - 12a) - (12a + 48)

3a(a - 4) -(12a + 48)

3a(a - 4) -12(a - 4)

(3a - 12)(a - 4)

combining the numerator

and denominator gives

= $\frac{3(a-4)(a+4)}{(3a-12)(a-4)}$

= $\frac{3(a-4)(a+4)}{3(a-4)(a-4)}$

= $\frac{(a+4)}{(a-4)}$

---

johnmulu answered the question on March 8, 2017 at 13:29

Next:  Two points P and Q lies on latitude 65 ²S. Their longitudes are 96 ²E and 84 ²W respectively. Find the distance between them in km. Take R = 6370 km and $\pi = 3.142$
Previous: The positions of two towns X and Y are given to the nearest degree as X(45^oN, 10^oW) and Y(45^oN, 70^oW). Find

View More Mathematics Questions and Answers | Return to Questions Index

Exams With Marking Schemes

• Grade 1
• Grade 2
• Grade 3
• Grade 4
• Grade 5
• Grade 6
• Grade 7
• Grade 8
• Grade 9
• PP1
• PP2
• Playgroup
• Form 1
• Form 2
• Form 3
• Form 4

Related Questions

• Two points P and Q lies on latitude 65 ²S. Their longitudes are 96 ²E and 84 ²W respectively. Find the distance between them in km. Take R = 6370 km and $\pi = 3.142$(Solved)
  

  Two points P and Q lies on latitude 65 ²S. Their longitudes are 96 ²E and 84 ²W respectively. Find the distance between them in km. Take R = 6370 km and $\pi = 3.142$

  Date posted: March 8, 2017.  Answers (1)

• Calculate the area enclosed between the curve y = 6x - x² x –axis and the lines x = 1 and x = 5 using...(Solved)
  

  Calculate the area enclosed between the curve y = 6x - x² x –axis and the lines x = 1 and x = 5 using the mid-ordinate rule with four strips

  Date posted: March 8, 2017.  Answers (1)

• Calculate the area enclosed between the curve y = 6x - x², x - axis and the lines x = 1 and x = 5 using the mid-ordinate rule with four strips(Solved)
  

  Calculate the area enclosed between the curve y = 6x - x², x - axis and the lines x = 1 and x = 5 using the mid-ordinate rule with four strips

  Date posted: March 8, 2017.  Answers (1)

• Intersection point of the lines of equations 2x – 3y = -29 and circle whose radius is 5 units. Find the equation of the circle(Solved)
  

  Intersection point of the lines of equations 2x – 3y = -29 and circle whose radius is 5 units. Find the equation of the circle

  Date posted: March 8, 2017.  Answers (1)

• Given (1 – 3x)⁵ Determine the number of terms in the expansion(Solved)
  

  Given (1 – 3x)⁵
  a) Determine the number of terms in the expansion
  b) Expand (1 - 3)⁵ and use your expansion to estimate (0.97)⁵ correct to 4 significant figures
  

  Date posted: March 8, 2017.  Answers (1)

• Solve the equation log₃(x + 23) - log₃(log₂32) = log₃(9 - 2x)(Solved)
  

  Solve the equation
  log₃(x + 23) - log₃(log₂32) = log₃(9 - 2x)

  Date posted: March 8, 2017.  Answers (1)

• Given that P = 4 + $\sqrt2$ and that $\frac{P}{Q}$ = a + b$\sqrt c$ where a, b and c are constants, find the values of a, b and c (Solved)
  

  Given that P = 4 + $\sqrt2$ and that
  $\frac{P}{Q}$ = a + b$\sqrt c$ where a, b and c are constants, find the values of a, b and c

  Date posted: March 8, 2017.  Answers (1)

• A ship leaves an island (5^o, 45^oE) and sails due east for 120 hours to another island. The average speed of the ship is 27 knots(Solved)
  

  A ship leaves an island (5^o, 45^oE) and sails due east for 120 hours to another island. The average speed of the ship is 27 knots
  a) Calculate the distance between the two islands
  i) in nautical miles
  ii) in kilometres
  b) Calculate the speed of the ship in kilometres per hour
  c) Find the position of the second island. (Take 1 nm to be 1.853 km and the radius of the earth to be 6370 km)

  Date posted: March 8, 2017.  Answers (1)

• A stone is thrown vertically upwards such that its height is S metres above the ground after t seconds is given by s = 40t - 10t². Find(Solved)
  

  A stone is thrown vertically upwards such that its height is S metres above the ground after t seconds is given by s = 40t - 10t².
  Find
  i) The height above the ground after 2 seconds
  ii) The velocity after 1 second
  iii) The instant at which the stone is 30 m high

  Date posted: March 8, 2017.  Answers (1)

• A solid cone of height 12 cm and radius 9 cm is recast into a solid sphere. Calculate the surface area of the sphere(Solved)
  

  A solid cone of height 12 cm and radius 9 cm is recast into a solid sphere. Calculate the surface area of the sphere

  Date posted: March 8, 2017.  Answers (1)

• Solve the simultaneous equations x² + y² = 26 x + y = 4(Solved)
  

  Solve the simultaneous equations
  x² + y² = 26
  x + y = 4

  Date posted: March 8, 2017.  Answers (1)

• A G.P has third term 24 and sixth term 192. Determine the first term and the common ratio(Solved)
  

  A G.P has third term 24 and sixth term 192. Determine the first term and the common ratio

  Date posted: March 8, 2017.  Answers (1)

• Differentiate y = (x + 2)(x - 1) with respect x (Solved)
  

  Differentiate y = (x + 2)(x - 1) with respect x

  Date posted: March 8, 2017.  Answers (1)

• Determine the centre and radius of a circle given by the equation $2x^2\;+\;2y^2\;-\;12\;=\;4x\;-\;12y$(Solved)
  

  Determine the centre and radius of a circle given by the equation
  $2x^2\;+\;2y^2\;-\;12\;=\;4x\;-\;12y$

  Date posted: March 8, 2017.  Answers (1)

• Solve for y given that $log_2(2y\; + \;3)-\;2\; = log_2(y - 2)$ (Solved)
  

  Solve for y given that
  $log_2(2y\; + \;3)-\;2\; = log_2(y - 2)$
  

  Date posted: March 8, 2017.  Answers (1)

• Evaluate (3 - $\sqrt7$)(3 + $\sqrt7$) hence simplify $\frac{2}{3\; -\sqrt7}$ - $\frac{2}{3\; +\sqrt7}$(Solved)
  

  Evaluate (3 - $\sqrt7$)(3 + $\sqrt7$) hence simplify
  $\frac{2}{3\; -\sqrt7}$ - $\frac{2}{3\; +\sqrt7}$

  Date posted: March 7, 2017.  Answers (1)

• The sides of triangles were measured and recorded as 8.4 cm, 10.5 cm and 15.3 cm. Calculate the percentage error in perimeter (Solved)
  

  The sides of triangles were measured and recorded as 8.4 cm, 10.5 cm and 15.3 cm. Calculate the percentage error in perimeter correct to 2 decimal places

  Date posted: March 7, 2017.  Answers (1)

• The equation of a curve is y = 3x² -4x + 1, Find the gradient function of the curve and its value when x = 2(Solved)
  

  The equation of a curve is
  y = 3x² -4x + 1
  a) Find the gradient function of the curve and its value when x = 2
  b) Determine the equation of the tangent to the curve at(2,5)

  Date posted: March 7, 2017.  Answers (1)

• a) The nth term of a sequence is given as 3^{(m + 1)} - 2m.(Solved)
  

  a) The nth term of a sequence is given as 3^{(m + 1)} - 2m. Find the 5th term of the sequence
  b) Atieno was employed by NGO on contract for a certain number of years. Her basic annual salary for the first year was sh 580 000 and her last basic annual salary was sh 630 400. By end of contract she had earned a total basic salary of sh 4 841 600. If the annual increment was constant, calculate
  i) The period of the contract
  ii) The annual increment
  iii) The annual basic salary in the third year of contract
  

  Date posted: March 7, 2017.  Answers (1)

• Expand (2 + 2x)⁵ in ascending powers of x up to the term x³ (Solved)
  

  a) Expand (2 + 2x)⁵ in ascending powers of x up to the term x³
  b) Hence use your expansion in a) above to evaluate (2.03)⁵ to 3 s.f.
  

  Date posted: March 7, 2017.  Answers (1)