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

`((1)/(x-3)+(4)/(x))/((4)/(x)-(1)/(x-3))`

To find:

The simplified form of given expression.

Solution:

We have,

`((1)/(x-3)+(4)/(x))/((4)/(x)-(1)/(x-3))`

`=((1(x)+4(x-3))/((x-3)x))/((4(x-3)-1(x))/(x(x-3)))`

`=(x+4x-12)/((x-3)x)* (x(x-3))/(4x-12-x)`

`=(5x-12)/(3x-12)`

`=(5x-12)/(3(x-4))`

Therefore, the last option is correct, i.e.,
`(5x-12)/(3(x-4))`.