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

Answer:

Option A is correct

$\frac{2x^2+49}{x(x-7)}$

Step-by-step explanation:

Given that:

$\frac{3x}{x-7}-\frac{x+7}{x}$

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

then;

$\frac{3x(x)-(x+7)(x-7)}{x(x-7)}$

Using identity rule:

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

⇒$\frac{3x^2-(x^2-7^2)}{x(x-7)}$

⇒$\frac{3x^2-(x^2-49)}{x(x-7)}$

Remove the bracket

⇒$\frac{3x^2-x^2+49}{x(x-7)}$

Combine like terms:

⇒$\frac{2x^2+49}{x(x-7)}$

Therefore, $\frac{2x^2+49}{x(x-7)}$ is equivalent to $\frac{3x}{x-7}-\frac{x+7}{x}$