SOLUTION: Perform the indication functions. 14x-7/x^2+3x-4 * x^2+6x+8/2x^2+5x-3 / x^2+2x/x^2+2x-3

Algebra ->  Rational-functions -> SOLUTION: Perform the indication functions. 14x-7/x^2+3x-4 * x^2+6x+8/2x^2+5x-3 / x^2+2x/x^2+2x-3       Log On


   

Question 119220: Perform the indication functions.
14x-7/x^2+3x-4 * x^2+6x+8/2x^2+5x-3 / x^2+2x/x^2+2x-3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!



Let's simplify the numerator %2814x-7%29%2F%28x%5E2%2B3x-4%29%2A%28x%5E2%2B6x%2B8%29%2F%282x%5E2%2B5x-3%29




%28%2814x-7%29%2F%28x%5E2%2B3x-4%29%29%28%28x%5E2%2B6x%2B8%29%2F%282x%5E2%2B5x-3%29%29 Start with the given expression

%28%287%282x-1%29%29%2F%28x%5E2%2B3x-4%29%29%28%28x%5E2%2B6x%2B8%29%2F%282x%5E2%2B5x-3%29%29 Factor 14x-7 to get 7%282x-1%29

Factor x%5E2%2B3x-4 to get %28x%2B4%29%28x-1%29

Factor x%5E2%2B6x%2B8 to get %28x%2B4%29%28x%2B2%29

Factor 2x%5E2%2B5x-3 to get %28x%2B3%29%282x-1%29


7%282x-1%29%28x%2B4%29%28x%2B2%29%2F%28x%2B4%29%28x-1%29%28x%2B3%29%282x-1%29 Combine the fractions


Cancel like terms


7%28x%2B2%29%2F%28x-1%29%28x%2B3%29 Simplify





So %28%2814x-7%29%2F%28x%5E2%2B3x-4%29%29%28%28x%5E2%2B6x%2B8%29%2F%282x%5E2%2B5x-3%29%29 simplifies to 7%28x%2B2%29%2F%28x-1%29%28x%2B3%29. In other words


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So becomes


%287%28x%2B2%29%2F%28x-1%29%28x%2B3%29%29%2F%28%28x%5E2%2B2x%29%2F%28x%5E2%2B2x-3%29%29


%287%28x%2B2%29%2F%28x-1%29%28x%2B3%29%29%2A%28%28x%5E2%2B2x-3%29%2F%28x%5E2%2B2x%29%29 Multiply the first fraction by the reciprocal of the second fraction



Factor x%5E2%2B2x-3 to get %28x%2B3%29%28x-1%29

Factor x%5E2%2B2x to get x%28x%2B2%29


7%28x%2B2%29%28x%2B3%29%28x-1%29%2F%28x-1%29%28x%2B3%29x%28x%2B2%29 Combine the fractions



Cancel like terms


7%2Fx Simplify






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Answer:



So simplifies to 7%2Fx



In other words,