Adding Rational Expressions
Use the example and the procedures you wrote to add the following rational expressions:
- \(\dfrac{1}{x+3}+\dfrac{1}{x+5}\)
- \(\dfrac{2}{x+7}+\dfrac{3}{x+7}\)
- \(\dfrac{3+x}{x+7}+\dfrac{4+x}{x+5}\)
- \(\dfrac{x-3}{x+8}+\dfrac{x+1}{x-6}\)
Answers:
(Check to see if you have the right answers which are listed below. They are not in order, and there is one extra answer.)
\(\dfrac{2x^2+26}{x^2+2x-48} \hspace{5mm} \dfrac{5}{x+7} \hspace{5mm} \dfrac{2x^2+19x+43}{x^2+12x+35} \hspace{5mm} \dfrac{x^2+26}{x^2+2x-48} \hspace{5mm} \dfrac{2x+8}{x^2+8x+15}\)
What did you notice? For extra practice try the same procedures with some subtraction problems. Don’t forget to distribute the subtraction sign to the terms in the subtrahend.
