Question

Simplify 1 over quantity x minus 3 plus 4 over x all over 4 over x minus 1 over quantity x minus 3 . (2 points) 5 over 3 5 x minus 3 over 3 open parentheses x minus 1 close parentheses 1 5 x minus 12 over 3 open parentheses x minus 4 close parentheses

Answer 1

Given:

Expression is

$\dfrac{\dfrac{1}{x-3}+\dfrac{4}{x}}{\dfrac{4}{x}-\dfrac{1}{x-3}}$

To find:

The simplified form of given expression.

Solution:

We have,

$\dfrac{\dfrac{1}{x-3}+\dfrac{4}{x}}{\dfrac{4}{x}-\dfrac{1}{x-3}}$

$=\dfrac{\dfrac{1(x)+4(x-3)}{(x-3)x}}{\dfrac{4(x-3)-1(x)}{x(x-3)}}$

$=\dfrac{x+4x-12}{(x-3)x}\times \dfrac{x(x-3)}{4x-12-x}$

$=\dfrac{5x-12}{3x-12}$

$=\dfrac{5x-12}{3(x-4)}$

Therefore, the last option is correct, i.e., $\dfrac{5x-12}{3(x-4)}$.