Question

3/x+2 +2/x-2=8/(x+2)(x-2)
Solve and tell if its extraneous

Answer 1

@Hero

Answer 2

now you can have extraneous solutions because you have denominators

Answer 3

:)

Answer 4

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

Answer 5

multiply

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

ok and if \(x^2=4\) then \(x=?\)

Answer 11

x=+ or - 2

Answer 12

right

Answer 13

and in this case

Answer 14

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

Answer 15

:) Thanks!

Answer 16

yw