I need some help on a math problem?

Question

solve for x

1/(x+2) - 1/(x-3) = 5

Answer 1

1. start w/ fraction busters. multiply the whole thing by (x+2)(x-3).

2. this leaves you with (x-3) - (x+2) = 5(x+2)(x-3)

3. foil out the right side so you get (x-3) - (x+2) = 5(x^2 - x - 6)

4. distribute the 5: (x-3) - (x+2) = 5x^2-5x-30

5. distribute the minus on the left side: (x-3) + (-x-2) = 5x^2-5x-30

6. combine like terms: -5= 5x^2-5x-30

7. add the 5: 5x^2-5x-25=0

8. divide by lcm (5): x^2 - x - 5 = 0

9. factor: (x+2)(x-3)=0

10. zero product property: x=3, -2

i'm pretty sure that's right....

Answer 2

x - 3 - x - 2 = 5 ( x + 2) (x - 3)

-5 = 5 x² - 5x - 30

-1 = x² - x - 6

x² - x - 5 = 0

Using quadratic formula

we get x = 1/2 ± sqrt(21)/2

.

(-2 and 3 are clearly not solutions,

since either one makes for division by 0

in the original equation.)