## lindseyharrison 2 years ago What is the solution to the rational equation 3/2 - 1/x+5 = -2/2x + 10

1. lindseyharrison

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2. lindseyharrison

x = -5 x = -5/2 x = 5 No solution

3. campbell_st

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

4. lindseyharrison

It's no solution

5. campbell_st

correct

6. CliffSedge

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.