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Express (x - 2 over x + 1) - (5 over x-1) as a single fraction.
I had managed to get (x^2 - 6 x - 7 over x^2 - 1). I dont know where I am going wrong.
The correct answer is (x^2 - 8x - 3 over x^2 - 1).
Can someone please fully explain how to express this equation as a single fraction?
[(x - 2) / (x + 1)] - [5 / (x - 1)]
Firstly, we have to convert the fractions to a common denominator:
a/b - c/d = (a/b)(d/d) - (c/d)(b/b)
d/d and b/b are the ingenious elements of the equivalence class with the value "1". This applied to our problem yields:
[(x - 2) / (x + 1)] * [(x - 1) / (x - 1)] - [5 / (x - 1)] * [(x + 1) / (x + 1)]
{[(x - 2) * (x - 1)] / (x² - 1)} - {[5 * (x + 1)] / (x² - 1)}
[(x² - x - 2x + 2) - (5x + 5)] / (x² - 1)
Mind the sign convention in the next step when you get rid of the brackets
(x ² - 3x + 2 - 5x - 5) / (x² - 1)
(x² - 8x - 3) / (x² - 1).
I am sorry, but the book / the teacher was right.
