We need to get a common denominator for
#3/(2x+10)+5/4=7/(x+5)#
First, let's factor the denominators and see the components:
#3/(2(x+5))+5/(2*2)=7/(x+5)#
The common denominator will be #4(x+5)#
The first fraction needs a #2#, and if we multiply the second fraction (top and bottom) by #(x+5)# we should have a good start:
#3/(2(x+5))*(2)/(2)+5/(2*2)*(x+5)/(x+5)=7/(x+5)#
#6/(4(x+5))+(5x+25)/(4(x+5))=(7)/(x+5)#
Let's combine the two fractions:
#(6+5x+25)/(4(x+5))=7/(x+5)#
If we multiply #7/(x+5)# by #4/4#, both fractions will have the same denominator:
#(6+5x+25)/(4(x+5))=28/(4(x+5))#
Multiply by #(4(x+5))# on both sides and cancel denominators
#6+5x+25=28#
Combine like-terms
#31+5x=28#
Subtract #31# on both sides
#5x=-3#
Divide by #5# on both sides
#x=-3/5#
