How do you solve #\frac { 8} { 3} = \frac { m - 5} { m - 10}#?

#8/3=(m-5)/(m-10)#

Multiply both sides by #3(m-10)#.

#3(m-10)xx8/3=3(m-10)xx(m-5)/(m-10)#

#cancel3(m-10)xx8/cancel3=3cancel((m-10))xx(m-5)/cancel(m-10)#

#(m-10)xx8=3xx(m-5)#

Open the brackets and simplify.

#8m-80=3m-15#

Subtract #3m# from each side.

#8m-3m-80=3m-3m-15#

#5m-80=-15#

Add #80# to each side.

#5m+80-80=80-15#

#5m=65#

Divide both sides by #5#.

#(5m)/5=65/5#

#(cancel5m)/cancel5=(13cancel65)/(1cancel5)#

#m=13#

Solve:

#8/3=(m-5)/(m-10)#

Cross multiply. Multiply the denominators by the numerators of the opposite fractions.

#(8(m-10))/(3(m-5))#

Expand.

#8m-80=3m-15#

Subtract #3m# from both sides.

#8m-80-3m=3m-3m-15#

Cancel #3m# on the right side.

#8m-80-3m=color(red)cancel(color(black)(3m))-color(red)cancel(color(black)(3m))-15#

Simplify.

#5m-80=-15#

Add #80# to both sides.

#5m-80+80=-15+80#

Cancel #80# on the left side.

#5m-color(red)cancel(color(black)(80))+color(red)cancel(color(black)(80))=-15+80#

Simplify.

#5m=65#

Divide both sides by #5#.

#(5m)/5=65/5#

Cancel #5# on the left side.

#(color(red)cancel(color(black)(5^1))m)/color(red)cancel(color(black)(5^1))=65/5#

Simplify.

#m=13#