Solve for x:-

Asked by saketagarwal.dbl | 17th Jan, 2017, 05:35: PM

Expert Answer:

begin mathsize 16px style fraction numerator a over denominator x minus a end fraction plus fraction numerator b over denominator x minus b end fraction equals fraction numerator 2 c over denominator x minus c end fraction
rightwards double arrow fraction numerator a left parenthesis x minus b right parenthesis plus b left parenthesis x minus a right parenthesis over denominator left parenthesis x minus a right parenthesis left parenthesis x minus b right parenthesis end fraction equals fraction numerator 2 c over denominator x minus c end fraction
rightwards double arrow left parenthesis x minus c right parenthesis left square bracket a left parenthesis x minus b right parenthesis plus b left parenthesis x minus a right parenthesis right square bracket equals 2 c left parenthesis x minus a right parenthesis left parenthesis x minus b right parenthesis
rightwards double arrow left parenthesis x minus c right parenthesis left parenthesis a x minus a b plus b x minus a b right parenthesis equals 2 c left parenthesis x squared minus b x minus a x plus a b right parenthesis
rightwards double arrow a x squared minus a b x plus b x squared minus a b x minus a c x plus a b c minus b c x plus a b c equals 2 c x squared minus 2 b c x minus 2 a c x plus 2 a b c
rightwards double arrow a x squared minus 2 a b x plus b x squared minus a c x plus 2 a b c minus b c x equals 2 c x squared minus 2 b c x minus 2 a c x plus 2 a b c
rightwards double arrow a x squared plus b x squared minus 2 c x squared equals 2 a b x minus a c x minus b c x
rightwards double arrow left parenthesis a plus b minus 2 c right parenthesis x squared equals x left parenthesis 2 a b minus a c minus b c right parenthesis
rightwards double arrow left parenthesis a plus b minus 2 c right parenthesis x squared minus x left parenthesis 2 a b minus a c minus b c right parenthesis equals 0
rightwards double arrow x left square bracket left parenthesis a plus b minus 2 c right parenthesis x minus left parenthesis 2 a b minus a c minus b c right parenthesis right square bracket equals 0
rightwards double arrow x equals 0 space o r space left parenthesis a plus b minus 2 c right parenthesis x minus left parenthesis 2 a b minus a c minus b c right parenthesis space equals space 0
rightwards double arrow x equals 0 space o r space left parenthesis a plus b minus 2 c right parenthesis x equals left parenthesis 2 a b minus a c minus b c right parenthesis space
rightwards double arrow x equals 0 space o r space x equals fraction numerator left parenthesis 2 a b minus a c minus b c right parenthesis over denominator left parenthesis a plus b minus 2 c right parenthesis end fraction
end style

Answered by Rashmi Khot | 18th Jan, 2017, 09:14: AM