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

1 Answer
Oct 18, 2017

Answer:

#color(magenta)(y=1/5 or x=4#

Explanation:

#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#