Solving+Rational+Functions

EX. 1

x+3 / x+1 = x-2 / x-3

(x+3 / x+1) - (x-2 / x-3) = 0

(x+3)(x-3) - (x-2)(x+1) / (x+1)(x-3) = 0

x^2 - 9 - (x^2 - x - 2) / (x+1)(x-3) = 0

(x^2 - 9 - x^2 + x + 2) / (x+1)(x-3) = 0

(x - 7) / (x+1)(x-3) = 0

x = 7

x ≠ 1, 3

EX. 2

(2 / x) - (4 / x - 2) = 5

(2 / x) - (4 / x-2) - 5 = 0

2(x-2) / x(x-2) - 4x / x(x-2) - 5x(x-2) / x(x-2) = 0

-5x^2 + 8x - 4 / x(x-2) = 0

NO SOLUTION


 * Solving Rational Functions **
 * By: Megan ... October 25 **

EX 3

1/x + 4/x+1 = 6/x^2 - 3

x/x^2 + 4/x+1 - 6/x^2 + 3 = 0

x-6/x^2 + 4/x+1 + 3 = 0

(x-6)(x+1)+3x^2(x+1)+4x^2 / (x^2)(x+1) = 0

x^2 - 5x - 6 + 3x^2 + 4x^2 / (x^2)(x+1)

(x+1)(3x+2)(x+3) / (x^2)(x+1) = 0

x ≠ 0, -1 x = 1, -2/3 , -3

Here's a link explaining more on solving rational functions.

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