How do you subtract and simplify #\frac { 7s } { ( 25s ^ { 2} - 16t ^ { 2} ) } - \frac { s } { ( 5s - 4t ) }#?

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Answer 1 · 2017-08-18T11:31:03

#(s(7-5s-4t))/((5s-4t)(5s+4t))#

start by factorising the denominator of the first fraction by difference of squares

#(7s)/(25s^2-16t^2)-s/(5s-4t)#

#=(7s)/((5s-4t)(5s+4t))-s/(5s-4t)#

now make the denominator of the second the same as teh first by multiplying top and bottom by #(5s+4t)#

#=(7s)/((5s-4t)(5s+4t))-(s(5s+4t))/((5s-4t)(5s+4t))#

now subtract the numerators over the common denominator

#=(7s-s(5s+4t))/((5s-4t)(5s+4t))#

now simplify

#=(s(7-5s-4t))/((5s-4t)(5s+4t))#