How do you solve #(5x-4)/(5x+4) = 2/3#?

Question

3630 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-09-06T20:12:10

#x = 4#

If an equation has ONE FRACTION on each side, we can get rid of the fractions by cross-multiplying.

#color(blue)((5x-4))/color(lime)((5x+4)) = color(lime)(2)/color(blue)(3)#

#color(blue)(3xx(5x-4)) = color(lime)(2xx(5x+4) " "larr # no fractions!

#15x-12 = 10x+8#

#15x-10x = 8+12#

#5x = 20#

#x = 4#

Answer 2 · 2016-09-06T20:15:32

#x=4#

#(5x-4)/(5x+4)=2/3#

We crossmutliply first:

i.e. #3(5x-4)=2(5x+4)#

#15x-12=10x+8#

And then subtract #10x+8# from both sides of the equation:

#5x-20=4#, and thus #x=4#.