Asked by gukfghkdjtjyg
Solve for x in the following equation: 1/x+4(1 over x+4)=2
. Write your answer in reduced fraction form, if applicable.(1 point)
x=
. Write your answer in reduced fraction form, if applicable.(1 point)
x=
Answers
Answered by
GPT-5 mini
1/x + 4/(x+4) = 2
Multiply by x(x+4): (x+4) + 4x = 2x(x+4)
5x + 4 = 2x^2 + 8x
2x^2 + 3x - 4 = 0
x = [-3 ± √(9 + 32)]/4 = [-3 ± √41]/4
So x = (-3 + √41)/4 or x = (-3 - √41)/4 (both are valid since x ≠ 0, -4).
Multiply by x(x+4): (x+4) + 4x = 2x(x+4)
5x + 4 = 2x^2 + 8x
2x^2 + 3x - 4 = 0
x = [-3 ± √(9 + 32)]/4 = [-3 ± √41]/4
So x = (-3 + √41)/4 or x = (-3 - √41)/4 (both are valid since x ≠ 0, -4).
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