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

$-7=x$

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