Question

Perform the indicated operations and simplify.
((x^2-9)/(x+4)*(2x+8)/(x+5))÷(2x-6)/(x+1)
a. x^2+3/x+5 b. x^2-2x-3/x+5 c. x^2+4x+3/x+5 d. (x^2-9)(4x-12)/(x+5)(x+1)

Answer 1

Do factorization, simplify....
Use the identity a^2 - b^2 = (a+b)(a-b)
By the way, is the question like this ?
\[\large \frac{((x^2-9)}{(x+4)}\times \frac{(2x+8)}{(x+5})÷\frac{(2x-6)}{(x+1)}\]

Answer 2

yes its like that except the first parentheses is on the outside of the first fraction like it is beside the division symbol

Answer 3

Sorry... I was away and I'm back :|
\[\large (\frac{(x^2-9)}{(x+4)}\times \frac{(2x+8)}{(x+5})÷\frac{(2x-6)}{(x+1)}\]\[=\large (\frac{(x-3)(x+3)}{(x+4)}\times \frac{2(x+4)}{x+5})÷\frac{2(x-3)}{(x+1)}\]\[=\large \frac{(x-3)(x+3)}{(x+4)}\times \frac{2(x+4)}{x+5}\times \frac{(x+1)}{2(x-3)}\]\[=\large \frac{2(x-3)(x+3)(x+4)(x+1)}{2(x+4)(x+5)(x-3)}\]Now, cross out the common factors in the numerator and denominator... Can you get the answer?!

Answer 4

no dont really understand cross multiplication @Callisto

Answer 5

Eh..?! Just simple multiplication... I don't think cross multiplication is applied here..