Question

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

Answer 1

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

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 }`

Answer 2

Answer:
`(6-x)/(x^(2)-2x)`

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:

`(2x-3(x-2))/(x(x-2))`

Apply the distributive property, then you obtain:

`(2x-3x+6)/(x^(2)-2x)`

Add like terms, then you obtain:

`(6-x)/(x^(2)-2x)`