Find all real x where
2 \cdot \frac{x - 5}{x - 3} > \frac{2x - 5}{x + 2} + 20.
Give your answer in interval notation.
Find all real x for
I II
2⋅x−5x−3>2x−5x+2+20.f(x)=2⋅x−5x−3−2x−5x+2−20>02(x−5)(x+2)−(2x−5)(x−3)−20(x−3)(x+2)>0(2x−10)(x+2)−(2x2−6x−5x+15)−20(x2+2x−3x−6)>0
2x2+4x−10x−20−2x2+11x−15−20x2−40x+60x+120>0f(x)=−20x2+25x+85>0
x1,2=−b±√b2−4ac2ax1,2=−25±√252+4⋅20⋅85−40x0∈{−1.5292,2.7792}
The extreme points of the hyperbolas I and II are xI=3 and xII=−2.
In the calculated range is(2⋅x−5x−3) < (2x−5x+2+20)x∈R (−1.52921099245<x<2.77921099245)
The extreme points of the hyperbolas I and II are xI=3 and xII=−2.This gives:(2⋅x−5x−3) > (2x−5x+2+20)x∈R(−2<−1.5292)andx=R(2.7792<3)
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