SOLUTION: 1/(x-4) + 1/(x+2) = 8/7 find x

Question 947573: 1/(x-4) + 1/(x+2) = 8/7
find x

Found 2 solutions by josgarithmetic, addingup:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Multiply the left and right sides by . Simplify...
Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
Let's bring the two together with the common denominator (x-4)(x+2):
2(x-1)/(x-4)(x+2)= 8/7. Cross multiply to clear the fractions:
14(x-1)= 8(x-4)(x+2)Expand out the terms on both sides:
14x-14= 8x^2-16x-64 Subtract 8x^2-16x-64 from both sides, and you get:
-8x^2+30x+50= 0 Factor the left hand side:
-2(x-5)(4x+5)=0 Divide both sides by -2:
(x-5)(4x+5)=0 Split into 2 equations:
x-5= 0 or 4x+5=0 On the left add 5 and on the left subtract 5, both sides:
x=5 or 4x= -5 Solve for x on the right, divide both sides by 4, and
Solution: x=5 or x= -5/4 which you can also write as -1 1/4

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