Question

What is the difference of the rational expressions below? 2/x-2 - 3/x

Answer 1

Answer: $\frac{6-x}{x^{2}-2x}$

Step-by-step explanation:

Find the least common multiple (LCM) of the denominators. This is:

$LCM=x(x-2)$

Divide the LCM by each denominator and multiply the result by each numerator, then you obtain:

$\frac{2x-3(x-2)}{x(x-2)}$

Apply the distributive property, then you obtain:

$\frac{2x-3x+6}{x^{2}-2x}$

Add like terms, then you obtain:

$\frac{6-x}{x^{2}-2x}$

Answer 2

Answer:

The correct answer is $\frac { 6 - x } { x^2 - 2x }$.

Step-by-step explanation:

We are given the following expression and we are to simplify it by finding the difference of these two rational terms:

$\frac {2} { x - 2 } - \frac { 3 } { x }$

Taking their LCM to get:

$\frac { 2x - 3 ( x - 2 )} { x ( x - 2 )}$

$\frac { 2x - 3x + 6 } { x^2 - 2x }$

$\frac { -x + 6 } { x^2 - 2x }$

$\frac { 6 - x } { x^2 - 2x }$