Question

Algebraic Fractions!

Simplify each of these by factorising and then cancelling;

A) X^2+X-12
---------------
X-3

B). 5x-25
-----------------
X^2-3x-10

C) X^2-16
--------------
X^2+2x-24
(If you can only help with one then that's fine )

Answer 1

A.
`(x^(2) + x - 12)/(x - 3) = (x^(2) + 4x - 3x - 12)/(x - 3) = (x(x) + x(4) - 3(x) - 3(4))/(x - 3) = (x(x + 4) - 3(x + 4))/(x - 3) = ((x + 4)(x - 3))/(x - 3) = x + 4`

B.
`(5x -25)/(x^(2) - 3x - 10) = (5(x) - 5(5))/(x^(2) - 5x + 2x - 10) = (5(x - 5))/(x(x) - x(5) + 2(x) - 2(5)) = (5(x - 5))/(x(x - 5) + 2(x - 5)) = (5(x - 5))/((x + 2)(x - 5)) = (5)/(x + 2)`

C.
`(x^(2) - 16)/(x^(2) + 2x - 24) = (x^(2) + 4x - 4x - 16)/(x^(2) + 6x - 4x - 24) = (x(x) + x(4) - 4(x) - 4(2))/(x(x) + x(6) - 4(x) - 4(6)) = (x(x + 4) - 4(x + 4))/(x(x + 6) - 4(x + 6)) = ((x - 4)(x + 4))/((x - 4)(x + 6)) = (x + 4)/(x + 6)`