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solve (x^2+7x+2)/(x-2)>2, x range?
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06 Jun 2021, 09:09
2
Let's Learn to Solve Inequalities!
\(\frac{x^2+7x+2}{x-2}>2\)
Take 2 to left hand side, we get
\(\frac{x^2+7x+2}{x-2} - 2 > 0\) => \(\frac{x^2+7x+2 - 2*(x-2) }{x-2}>0\) => \(\frac{x^2+7x+2 - 2x + 4 }{x-2}>0\) => \(\frac{x^2+5x+6}{x-2}>0\) => \(\frac{x^2+2x + 3x +6}{x-2}>0\) => \(\frac{x(x+2) + 3(x +2)}{x-2}>0\) => \(\frac{(x+2)* (x+3)}{x-2}>0\) Multiply numerator and denominator on left hand side by x-2 we get => \(\frac{(x+2)* (x+3) * (x-2)}{(x-2)^2}>0\) Denominator is \((x-2)^2\) which will anyways be > 0 so we can ignore this to solve the problem So, question reduces to (x+2)* (x+3) * (x-2) > 0
Re: solve (x^2+7x+2)/(x-2)>2, x range?
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28 Sep 2024, 21:08
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Re: solve (x^2+7x+2)/(x-2)>2, x range? [#permalink]