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lindseyharrison
What is the solution to the rational equation 3/2 - 1/x+5 = -2/2x + 10
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x = -5 x = -5/2 x = 5 No solution
ok... simplify the fraction on the rhs -2/(2x + 10) = -2/2(x + 5) = -1/(x + 5) so you have 3/2 - 1/(x + 5) = -1/(x + 5) add -1/(x + 5) to both sides for your solution
It's no solution
You don't need to simplify the right side. \[\frac{3}{2}-\frac{1}{x+5}=\frac{-2}{2x+10}.\] Simplify the left side: \[\frac{3}{2}-\frac{1}{x+5}=\frac{3x+13}{2x+10} .\] With same denominators, now you only need to solve the numerator equation, 3x+13=-2 which indeed has no solution because if x=-5 then division by zero.