Question

Which is equivalent to 3x/x-7 - x+7/x?

A) 2x^2+49/x(x-7)
B) x^2+49/x(x-7)
C) 2(x+7)/x(x-7)
D) 2(x-7)/x(x-7)

Answer 1

The answer is C, Hope I helped.

Answer 2

Option A is correct

`(2x^2+49)/(x(x-7))`

Explanation:

Given that:

`(3x)/(x-7)-(x+7)/(x)`

Take LCM of (x-7) and x is, x(x-7)

then;

`(3x(x)-(x+7)(x-7))/(x(x-7))`

Using identity rule:

`(a+b)(a-b)=a^2-b^2`

⇒
`(3x^2-(x^2-7^2))/(x(x-7))`

⇒
`(3x^2-(x^2-49))/(x(x-7))`

Remove the bracket

⇒
`(3x^2-x^2+49)/(x(x-7))`

Combine like terms:

⇒
`(2x^2+49)/(x(x-7))`

Therefore,
`(2x^2+49)/(x(x-7))` is equivalent to
`(3x)/(x-7)-(x+7)/(x)`