Quizzes & Puzzles75 mins ago
Maths Problem
27 Answers
I can't find a special section for Maths questions in Topics, so will post it here in the hope that someone can help. It is for a child whose teacher would not explain it to him (or give the answer!)
2x over x-1 minus 7x -3 over x squared - 1
The answer and bit of guidance with how to tackle the problem would be much appreciated.
2x over x-1 minus 7x -3 over x squared - 1
The answer and bit of guidance with how to tackle the problem would be much appreciated.
Answers
Best Answer
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For more on marking an answer as the "Best Answer", please visit our FAQ.If I can think back that far, with these sorts of questions I try multiplying throughout by the denominators, in order to get rid of the fractions. Then rearranging the terms obtained to try to make a quadratic, which is solved by any one of a number of ways, but commonly by using the usual equation.
use a common denominator of (x^2-1) = (x-1)(x+1)
2x/(x-1) = 2x(x+1)/((x-1)(x+1) = (2x^2+2x)/((x-1)(x+1))
1 = (x^2-1)/((x-1)(x+1))
thus the sum is (collecting all the numerators)
((2x^2+2x - (7x-3) - (x^2-1)) / ((x-1)(x+1))
= (2x^2 + 2x - 7x + 3 - x^2 + 1)/((x-1)(x+1))
= (x^2 - 5x + 4)/((x-1)(x+1)) =
= (x-1)(x+5)/((x-1)(x+1)) = (x+5)/(x+1)
2x/(x-1) = 2x(x+1)/((x-1)(x+1) = (2x^2+2x)/((x-1)(x+1))
1 = (x^2-1)/((x-1)(x+1))
thus the sum is (collecting all the numerators)
((2x^2+2x - (7x-3) - (x^2-1)) / ((x-1)(x+1))
= (2x^2 + 2x - 7x + 3 - x^2 + 1)/((x-1)(x+1))
= (x^2 - 5x + 4)/((x-1)(x+1)) =
= (x-1)(x+5)/((x-1)(x+1)) = (x+5)/(x+1)