Answer to Question #343472 in Algebra for Bethsheba Kiap

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Algebra

Question #343472

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)

Expert's answer

a. "\\frac{x^2+2x}{3x^2-18x+24}*\\frac{x^2-4x+4}{x^2-x-6}=\\\\"

"\\frac{x(x+2)}{3(x^2-6x+8)}*\\frac{(x-2)^2}{x^2-x-6}=\\\\\n=\\frac{x(x+2)}{3(x^2-6x+8)}*\\frac{(x-2)^2}{x^2-x-6}=\\\\\n=\\frac{x(x+2)}{3(x^2-2x-4x+8)}*\\frac{(x-2)^2}{x^2-3x+2x-6}=\\\\\n=\\frac{x(x+2)}{3(x-4)(x-2)}*\\frac{(x-2)^2}{(x-3)(x+2)}=\\\\\n=\\frac{x(x-2)}{3(x-4)(x-3)}"

b. "\\frac{(x^2+6x+9)}{x(x+3)}=\\frac{(x+3)^2}{x(x+3)}=\\frac{x+3}{x}"

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