## anonymous one year ago 3/x+2 +2/x-2=8/(x+2)(x-2) Solve and tell if its extraneous

1. anonymous

@Hero

2. anonymous

now you can have extraneous solutions because you have denominators

3. anonymous

:)

4. anonymous

$\frac{x}{x+2}+\frac{2}{x-2}=\frac{8}{(x+2)(x-2)}$ you have a choice, you can either add on the left, or multiply both sides by $$(x+2)(x-2)$$ to clear the fractions

5. anonymous

multiply

6. anonymous

ok then the $$(x+2)(x-2)$$ cancels on the right leaving $$8$$

7. anonymous

on the left the first term will be $$x(x-2)$$ and the second term will be $$2(x+2)$$

8. anonymous

by cancelling that leaves you with the equation $x(x-2)+2(x+2)=8$ multiply out and solve the resulting quadratic

9. anonymous

x^2-2x+2x+4=8 x^2+4=8 x^2=4

10. anonymous

ok and if $$x^2=4$$ then $$x=?$$

11. anonymous

x=+ or - 2

12. anonymous

right

13. anonymous

and in this case

14. anonymous

BOTH are extraneous, because both values would make the denominator equal to zero

15. anonymous

:) Thanks!

16. anonymous

yw