Question

What is the simplified sum of 3x/x-4 + x-3/2x

Answer 1

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▹ Answer

-1 - 1/2x

▹ Step-by-Step Explanation

3x ÷ x - 4 + x - 3 ÷ 2x

Divide and Rewrite:

3 * 1 - 4 + x - 3 ÷ 2 * x

Calculate:

3 - 4 + x - 3/2x

-1 + x - 3/2x

= -1 - 1/2x

Hope this helps!

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Answer 2

Explanation:

`(3x)/(x-4)+(x-3)/(2x)`

Make them into common denominators. To do so, multiply by the LCM of the denominators. The LCM of the denominators is (x-4)(2x). Thus, we multiply 2x to the first term and (x-4) to the second:

`((2x)/(2x)) (3x)/(x-4)+((x-4)/(x-4)) (x-3)/(2x)`

Simplify:

`(6x^2)/(2x(x-4))+(x^2-7x+12)/(2x(x-4)) \\=(7x^2-7x+12)/(2x(x-4))`

And this cannot be simplified further (you can also distribute the denominator if preferred).