Simplify (with Variables)?

Question

It is probably very easy and straightforward question. But I like to see how many ways you can do it. Please do one step at a time in separate lines and text not too "crowded" Thanks

1 / x-4 + 2 / x^2 -16 = 3 / x + 4

Answer 1

1 + 2 = 3
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x-4 x^2-16 (x+4)

1 + 2 = 3
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x-4 (x-4)(x+4) (x+4)

1(x+4) +2 = 3(x-4)
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(x-4)(x+4) lcd

x+4+2=3x-12
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(x-4)(x+4)

x+6=3x-12
x-x+6=3x-x-12
6=2x-12

6+12=2x-12+12
18=2x
x=9/(x-4)(x+4)

Answer 2

1/x-4 + 2 / x^2-16 = 3 / x+4 Factor x^2-16

1/x-4 + 2/(x+4)(x-4) = 3 / x+4 multiply through by (x-4)(x+4)

x + 4 + 2= 3 (x-4) Combine like terms

x + 6 = 3x - 12

-2x = -18

x = 9

To check put x = 9 back into original equation

1/5 + 2/ (81-16) = 3 / 13

1/5 + 2/ 65 = 3 /13

13/65 + 2 / 65 = 3/ 13

15/65 = 3/13 convert 15/65 to 3/13 (divide by 5)

3/13 = 3/13