Answer to Question #343246 in Algebra for bkay

Question

In the following problems, perform the operations and simplify as much as possible.

a. (x2 + 2x)/(3x2 – 18x + 24) ÷ (x2 – x – 6)/(x 2 – 4x + 4)

b. (x2 + 6x + 9)/x/(x + 3)

c. 1/(3x – 1) + x/(x2 – 9)

Answer 1

a. $\frac{(x^2+2x)}{\frac{(3x^2-18x+24)}{(x^2-x-6)/(x^2-4x+4)}}=\frac{x(x+2)}{\frac{3(x^2-6x+8)}{(x^2-x-6)/(x-2)^2}}=\frac{x(x+2)}{\frac{3}{1/(x-2)^2}}=\frac{x(x+2)(x-2)^2}{3}$

b.

$\frac{x^2+6x+9}{x/(x+3)}=\frac{(x+3)^2}{x/(x+3)}=\frac{(x+3)^3}{x}$

c.

$\frac{1}{3x-1}+\frac{x}{x^2-9}=\frac{x^2-9+x(3x-1)}{(3x-1)(x^2-9)}=\frac{4x^2-9-x}{(3x-1)(x^2-9)}$