Question

simplify each rational expresiion:
x^2-2x-24/x^2+7x+12 * x^2-1/x-6

Answer 1

First, factorise the expressions
x^2-2x-24 = x^2 - 6x + 4x - 24 = x(x-6) +4 (x-6) = (x+4)(x-6)
x^2+7x+12 = x^2 + 3x + 4x + 12 = x(x+3) + 4(x+3) = (x+4)(x+3)
x^2-1 = (x-1)(x+1) (Using the identity a^2-b^2 = (a+b)(a-b) )

Now, you can write this;
\[\frac{x^2-2x-24}{x^2+7x+12}\times \frac{ x^2-1}{x-6} = \frac{(x+4)(x-6)}{ (x+4)(x+3)}\times \frac{ (x-1)(x+1) }{x-6} \]Now, can you simplify the expression?

Answer 2

well i need to state any restrictions on the variable

Answer 3

Restriction:
the denominators of the fractions cannot be 0
So put the denominators =0 and solve x, that is
(x+4)(x+3) =0 or x-6= 0
x+4 =0 or x+3 =0 or x-6=0
Solve these 3 equations