Question

Simplify the expression. $$\frac{9}{4 x}+\frac{7}{-5 x}$$

Short answer

-17/20x

Step-by-step solution

Find the Common Denominator

To add or subtract fractions, you must have the same denominator, also known as the common denominator. This can be found by multiplying the individual denominators together. Therefore, the common denominator for the two fractions \(\frac{9}{4x}\) and \(\frac{7}{-5x}\) is -20x.

Rewrite the Fractions with the Common Denominator

Rewrite each fraction with the common denominator of -20x. Thus, \(\frac{9}{4x}\) becomes \(-\frac{9*5}{4x*-5}\) or, \(-\frac{45}{20x}\) and \(\frac{7}{-5x}\) becomes \(\frac{7*4}{-5x*4}\) or \(\frac{28}{20x}\).

Perform the Addition

Now that the denominators are the same, add the numerators together to get \(-\frac{45 + 28}{20x}\) which simplifies to \(\frac{-17}{20x}\).