How do you combine #\frac { 5y } { 5y - 1} - \frac { 1} { 1- 5y }# into one fraction?

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Answer 1 · 2017-06-25T23:55:58

Multiply to get a common denominator so that the fractions can be added. ( or in this case subtracted)

# {(5y) xx (1-5y)}/{(5y-1)xx(1-5y)} - {(1) xx (5y-1)}/ {(1-5y)xx (5y-1)}# This gives

#{ (5y - 25y^2) - (5y -1)}/ (-25y^2 + 10y -1) # adding common terms

# (-25y^2 + 0y +1 )/ (-25y^2 + 10y -1) # factoring the numerator and denominator gives

# {(-5y +1) ( +5y +1 )}/ {(-5y+1)xx(+5y -1) }# divide out #( -5y +1)# gives

# (5y +1)/(5y-1) #

Answer 2 · 2017-06-25T23:58:08

#(5y+1)/(5y−1)#

#-1(1-5y)=5y-1#

so #(5y)/(5y−1)-1/(1-5y)=(5y)/(5y−1)+1/(5y-1)#

since the denominators are now equal we can add the numerators and get #(5y+1)/(5y−1)#