Question

Solve the following equation and show all of your work for full credit. A correct answer without work show is worth only one point.


`(3)/(x-2) + (7)/(x+4) = (18)/(x^(2)+2x-8 )`

Answer 1

X=-8/5

Explanation:

Multiply all terms by (x-2)(x-4)(x+4) and cancel:

3(x−4)(x+4)+7(x−2)(x+4)=18(x−4)

10x2+14x−104=18x−72(Simplify both sides of the equation)

10x2+14x−104−(18x−72)=18x−72−(18x−72)(Subtract 18x-72 from both sides)

10x2−4x−32=0

2(5x+8)(x−2)=0(Factor left side of equation)

5x+8=0 or x−2=0(Set factors equal to 0)

x=

−8

5

or x=2

Check answers. (Plug them in to make sure they work.)

x=

−8

5

(Works in original equation)

x=2(Doesn't work in original equation)

Answer 2

There are no values of X , that make the equation true.

No solution

Explanation: