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

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carlosego carlosego · Answer 1 · 2019-03-02T20:02:17+01:00

Answer: [tex]\frac{6-x}{x^{2}-2x}[/tex]

Step-by-step explanation:

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

[tex]LCM=x(x-2)[/tex]

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

[tex]\frac{2x-3(x-2)}{x(x-2)}[/tex]

Apply the distributive property, then you obtain:

[tex]\frac{2x-3x+6}{x^{2}-2x}[/tex]

Add like terms, then you obtain:

[tex]\frac{6-x}{x^{2}-2x}[/tex]

alinakincsem alinakincsem · Answer 2 · 2019-03-02T22:44:48+01:00

Answer:

The correct answer is [tex] \frac { 6 - x } { x^2 - 2x } [/tex].

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:

[tex] \frac {2} { x - 2 } - \frac { 3 } { x } [/tex]

Taking their LCM to get:

[tex] \frac { 2x - 3 ( x - 2 )} { x ( x - 2 )} [/tex]

[tex] \frac { 2x - 3x + 6 } { x^2 - 2x } [/tex]

[tex] \frac { -x + 6 } { x^2 - 2x } [/tex]

[tex] \frac { 6 - x } { x^2 - 2x } [/tex]