Solve any solution is a real number. 6r2−10r+16−1r−2=r+105r−40

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Solve any solution is a real number.  6r2−10r+16−1r−2=r+105r−40

Richard Cheatham · Accepted Answer

Step 1  Given: the equation 6r2−10r+16−1r−2=r+105r−40  Step 2  Factor the expression r2−10r+16  r2−10r+16=r2−8r−2r+16  =r(r−8)−2(r−8)  =(r−2)(r−8)  Thus given equation can be written as  6(r−2)(r−8)−1r−2=r+105(r−8)  The least common denominator of the fraction is 5(r−2)(r−8).  Step 3   Make the denominator of each of the fractions the same as the least common denominator 5(r−2)(r−8).  6(5)5(r−2)(r−8)−5(r−8)5(r−2)(r−8)=(r+10)(r−2)5(r−2)(r−8)  30−5r+405(r−2)(r−8)=r2−2r+10r−205(r−2)(r−8)  70−5r5(r−2)(r−8)=r2+8r−205(r−2)(r−8)  Solve the equation for r,  70−5r−(r2+8r−20)5(r−2)(r−8)=0  That is −r2−13r+90=0.  r2+13r−90=0  r2+18r−5r−90=0  r(r+18)−5(r+18)=0  (r−5)(r+18)=0  Step 4  Either

Solve any solution is a real number. \frac{6}{r^{2}-10r+16}-\fr

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