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

What is the difference of the rational expressions below? 2/x-2 - 3/x-example-1

2 Answers

2 votes

Answer:

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 }

User Flo Edelmann
by
9.1k points
5 votes

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)

User Anish Ramaswamy
by
8.4k points

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