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

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Answer 1 · 2018-05-09T06:58:52

#x=-7#

Look at the LHS

#3/x-2/(x+4#

put them over a common denominator

#(3(x+4))/[x(x+4)]-[2(x)]/[x(x+4)]#

expand the brackets

#[3x+12-2x]/[x^2+4x]#

collect like terms

#[x+12]/[x^2+4x]#

so we now have

#5/[x^2+4x]=[x+12]/[x^2+4x]#

as they have the same denominators this means the numerators must be equal, as one fraction equals the other

#5=x+12#

subtract 12 from both sides

#-7=x#