SOLUTION: I am having a little difficulty with subtracting rational expressions. Specifically, it is the part after the factoring is complete and the numerators are being combined. The minus
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-> SOLUTION: I am having a little difficulty with subtracting rational expressions. Specifically, it is the part after the factoring is complete and the numerators are being combined. The minus
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Question 568486: I am having a little difficulty with subtracting rational expressions. Specifically, it is the part after the factoring is complete and the numerators are being combined. The minus sign is throwing me off. I know that the signs to the right of the minus sign change, but I'm having a little trouble with the combining. One of my problems is as follows:
2x-3/x+5-x^2-4x-19/x^2+8x+15
You can put this solution on YOUR website! Use parentheses so you can see what you are doing.
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(2x-3)/(x+5)-(x^2-4x-19)/(x^2+8x+15)
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Factor:
= (2x-3)/(x+5) - (x^2-4x-19)/[(x+5)(x+3)]
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LCD = (x+5)(x+3)
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Rewrite both factors with denominator = LCD
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= [(x+3)(2x-3)]/LCD - [x^2-4x-19]/LCD
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Combine the numerators over the LCD:
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= [2x^2+3x-9-x^2+4x+19]/LCD
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Simplify:
= [x^2+7x+10]/LCD
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Factor:
= [(x+5)(x+2)]/[(x+5)(x+3)]
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Cancel the common factor:
= (x+2)/(x+3)
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Cheers,
Stan H.
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