please i could use the help
1) solve for x:
4/x + 4/x2-9 = 3/x-3
2) solve for x:
5/x2-1 - 2/x = 2/x+1
thanks :]
1) solve for x:
4/x + 4/x2-9 = 3/x-3
2) solve for x:
5/x2-1 - 2/x = 2/x+1
thanks :]
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1. Find the LCD of x, x^2 -9, and x - 3 --> LCD = x(x^2 - 9)
Multiply both sides by LCD to clear out fractions:
4(x(x^2 - 9))/x + 4(x(x^2 - 9))/(x^2 - 9) = 3(x(x^2 - 9))/(x - 3)
Simplify: 4(x^2 - 9) + 4x = 3x(x + 3)
4x^2 - 36 + 4x = 3x^2 + 9x --> x^2 - 5x -36 = 0 --> (x - 9)(x + 4) = 0 --> x = 9 or -4
2. The LCD is (x^2 - 1)x
5(x(x^2 - 1))/(x^2 - 1) - 2(x(x^2 - 1))/x = 2(x(x^2 - 1))/(x + 1)
5x - 2(x^2 - 1) = 2x(x - 1)
5x - 2x^2 + 2 = 2x^2 - 2x
0 = 4x^2 - 7x - 2 --> 0 = (4x + 1)(x - 2) --> x = -1/4 or 2
Multiply both sides by LCD to clear out fractions:
4(x(x^2 - 9))/x + 4(x(x^2 - 9))/(x^2 - 9) = 3(x(x^2 - 9))/(x - 3)
Simplify: 4(x^2 - 9) + 4x = 3x(x + 3)
4x^2 - 36 + 4x = 3x^2 + 9x --> x^2 - 5x -36 = 0 --> (x - 9)(x + 4) = 0 --> x = 9 or -4
2. The LCD is (x^2 - 1)x
5(x(x^2 - 1))/(x^2 - 1) - 2(x(x^2 - 1))/x = 2(x(x^2 - 1))/(x + 1)
5x - 2(x^2 - 1) = 2x(x - 1)
5x - 2x^2 + 2 = 2x^2 - 2x
0 = 4x^2 - 7x - 2 --> 0 = (4x + 1)(x - 2) --> x = -1/4 or 2
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1).
4/x + 4/x2 - 9 = 3/x - 3
4(x ^2 - 9) + 4x = 3x(x + 3)
x^2 - 5x - 36 = 0
(x - 9)(x + 4) = 0
Solutions:
x = -4
x = 9
2).
5/(x2 - 1) - 2/x = 2/(x + 1)
5x - 2(x^2 - 1) = 2x(x - 1)
4x^2 - 7x - 2 = 0
(4x + 1)(x - 2) = 0
Solutions:
x = -1/4
x = 2
4/x + 4/x2 - 9 = 3/x - 3
4(x ^2 - 9) + 4x = 3x(x + 3)
x^2 - 5x - 36 = 0
(x - 9)(x + 4) = 0
Solutions:
x = -4
x = 9
2).
5/(x2 - 1) - 2/x = 2/(x + 1)
5x - 2(x^2 - 1) = 2x(x - 1)
4x^2 - 7x - 2 = 0
(4x + 1)(x - 2) = 0
Solutions:
x = -1/4
x = 2
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1. 1/12 ( 1+ - sqrt 97)
2. sqrt 7 -1.
2. sqrt 7 -1.