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Solve for x : 1/(x+1)+3/(5x+1)=5/(x+4),...

Solve for x : `1/(x+1)+3/(5x+1)=5/(x+4), x != -1,-1/5,-4

Text Solution

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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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