Solve for x:.  1/2x-3 + 1/x-5 = 10/9
 
 

Asked by Prafull Tiwary | 3rd Apr, 2017, 06:49: PM

Expert Answer:

begin mathsize 16px style fraction numerator 1 over denominator 2 straight x minus 3 end fraction plus fraction numerator 1 over denominator straight x minus 5 end fraction equals 10 over 9
rightwards double arrow fraction numerator straight x minus 5 plus 2 straight x minus 3 over denominator left parenthesis 2 straight x minus 3 right parenthesis left parenthesis straight x minus 5 right parenthesis end fraction equals 10 over 9
rightwards double arrow fraction numerator 3 straight x minus 8 over denominator left parenthesis 2 straight x minus 3 right parenthesis left parenthesis straight x minus 5 right parenthesis end fraction equals 10 over 9
rightwards double arrow 27 straight x minus 72 equals 10 left square bracket left parenthesis 2 straight x minus 3 right parenthesis left parenthesis straight x minus 5 right parenthesis right square bracket
rightwards double arrow 27 straight x minus 72 equals 10 left square bracket 2 straight x squared minus 10 straight x minus 3 straight x plus 15 right square bracket
rightwards double arrow 27 straight x minus 72 equals 10 left square bracket 2 straight x squared minus 13 straight x plus 15 right square bracket
rightwards double arrow 27 straight x minus 72 equals 20 straight x squared minus 130 straight x plus 150
rightwards double arrow 20 straight x squared minus 157 straight x plus 222 equals 0
So comma space straight a equals 20 comma space straight b equals negative 157 comma space straight c equals 222
So comma space straight x equals fraction numerator 157 plus-or-minus square root of left parenthesis negative 157 right parenthesis squared minus 4 left parenthesis 20 right parenthesis left parenthesis 222 right parenthesis end root over denominator 40 end fraction
rightwards double arrow space straight x equals fraction numerator 157 plus-or-minus square root of 24649 minus 17760 end root over denominator 40 end fraction
rightwards double arrow space straight x equals fraction numerator 157 plus-or-minus square root of 6889 over denominator 40 end fraction
rightwards double arrow space straight x equals fraction numerator 157 plus-or-minus 83 over denominator 40 end fraction
rightwards double arrow space straight x equals fraction numerator 157 plus 83 over denominator 40 end fraction space space or space space straight x equals fraction numerator 157 minus 83 over denominator 40 end fraction
rightwards double arrow space straight x equals 6 space space or space space straight x equals 1.85 end style

Answered by Rebecca Fernandes | 29th Nov, 2017, 02:25: PM