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# Solve

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Solve. Express answer using interval notation where appropriate. Check for extraneous solutions.

$$\frac{3x}{x+1}+\frac{5}{x-2}=\frac{15}{x^2-x-2}$$

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Express $$x^2-x-2 \text{ as }(x+1)(x-2)$$

Multiply every term by $$(x+1)(x-2) \text{ to get } 3x(x-2)+5(x+1)=15$$

Collect terms:  $$3x^2-x-10=0$$

Solve the quadratic to get $$x=-\frac{5}{3}\text{ and }x=2$$

2 is an extraneous solution (try substituting 2 into the original equation and see what you get!).

Alan  May 13, 2018
edited by Alan  May 13, 2018