Simplify algebraic expression
I posted a question before about simplifying an algebraic expression, but then I realised that I may have overcomplicated the answer. I got to the following equation initially:
$\frac{x^2-1(x+h)(x+h)}{x^2(x+h)(x+h)h}$
But at this point, I expanded the expression. Could I have just simplified this, and if so, how?
$\endgroup$ 12 Answers
$\begingroup$The denominator is nicely factored, leave it. For the numerator, either:
expand & simplify, then factor & simplify:$$\frac{x^2-(x^2+2xh+h^2)}{x^2(x+h)^2h}=-\frac{2xh+h^2}{x^2(x+h)^2h}=-\frac{(2x+h)h}{x^2(x+h)^2h}$$
factor using $a^2-b^2=(a-b)(a+b)$ and then simplify:$$\frac{x^2-(x+h)^2}{x^2(x+h)^2h}=\frac{(x-x-h)(x+x+h)}{x^2(x+h)^2h}=\frac{-h(2x+h)}{x^2(x+h)^2h}$$
You end up with:$$-\frac{2x+h}{x^2(x+h)^2}$$
$\endgroup$ 2 $\begingroup$It simplifies to $$\frac{x^2-(x^2+2hx+h^2)}{x^2h(x^2+2hx+h^2)}=\frac{-2x-h}{x^2(x+h)^2}$$
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