How do you solve $\frac{3}{y - 1} + \frac{1}{y} = \frac{5}{4}$ $\frac { 3} { y - 1} + \frac { 1} { y } = \frac { 5} { 4}$ ?

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Answer 1 · 2017-10-18T17:23:37

$y = \frac{1}{5} or x = 4$ $color(magenta)(y=1/5 or x=4$

$\frac{3}{y - 1} + \frac{1}{y} = \frac{5}{4}$ $3/(y-1)+1/y=5/4$

$:.(3(4y)+4(y-1)=5(y-1)(y))/((y-1)(y)(4))$

multiply both sides by $(y-1)(y(4))$

$:.12y+4y-4=5y^2-5y$

$:.5y^2-5y=16y-4$

$:.5y^2-21y+4=0$

$:.(5y-1)(y-4)=0$

$:.5y=1 or y=4$

$:.color(magenta)(y=1/5 or y=4$

~~~~~~~~~~~~~

check:-

substitute $color(magenta)(y= 0.2$

$3/((color(magenta)0.2)-1)+1/(color(magenta)0.2)=5/4$

$3/(0.2)+1/(0.2)=1.25$

$-3.75+5=1.25$

$color(magenta)(1.25=1.25$

substitute $color(magenta)(y=4$

$:.3/((color(magenta)4)-1)+1(color(magenta)4)=5/4$

$:.3/3+1/4=5/4$

$:.color(magenta)(1 1/4=1 1/4$

How do you solve \frac { 3} { y - 1} + \frac { 1} { y } = \frac { 5} { 4}3y−1+1y=54\frac { 3} { y - 1} + \frac { 1} { y } = \frac { 5} { 4}?