Question

For questions 19–23, add or subtract.
19. 8x over x+7 – 3 over x+7

20. 4 over x-5 + 1 over x-3

21. 2x+3 over x-4 + x-5 over x+2

22. 2 over 2x+1 – 3 over 5x+1

23. 2x+3 over x-4 – x-5 over x+2

Answer 1

Same as adding fractions. Find equivalent expressions in common terms (that is to say, rephrase the problem with a common denominator) and add or subtract the numerators. After you have added/subtracted, make sure your answer is simplified.

Answer 2

19. Already in common terms. Subtract the numerators.\[\frac{8x}{x+7} – \frac{3}{x+7} =\frac{8x-3}{x+7}\]

Answer 3

20. A little more complicated, since it isn't in common terms to start.\[\frac{4}{x-5} +\frac{1}{x-3} =\frac{4}{x-5}\frac{x-3}{x-3}+\frac{1}{x-3}\frac{x-5}{x-5}=\frac{4x-12}{(x-3)(x-5)}+\frac{x-5}{(x-3)(x-5)}\]\[=\frac{5x-17}{(x-3)(x-5)}\]

Answer 4

That should be enough to show you how....