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Solve for x : `1/(x+1)+3/(5x+1)=5/(x+4), x != -1,-1/5,-4 |
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Answer» We have, `(1)/(x+1)+(3)/(5x+1)=(5)/(x+4)` `(5x+1+3(x+1))/((x+1)(5x+1))=(5)/(x+4)` `implies(5x+1+3x+3)(x+4)=5(x+1)(5x+1)` `implies(8x+4)(x+4)=5(x+1)(5x+1)` `implies8x^(2)+32x+4x+16=5(5x^(2)+x+5x+1)` `implies8x^(2)+36x+16=25x^(2)+30x+5` `implies17x^(2)-17x+11x-11=0` `implies17x(x-1)+11(x-1)=0` `implies(x-1)(17+11)=0` :.Either `x-1=0or17x+11=0` `:.x=1orx=(-11)/(17)` |
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