Question 1209258
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The denominators are (x+5) and x
The LCD is x(x+5)


Multiply both sides by the LCD to clear out the fractions.
{{{(x+4)/(x+5) = (x-3)/x + (2x-7)/(x+5)}}}


{{{x(x+5)*((x+4)/(x+5)) = x(x+5)*((x-3)/x + (2x-7)/(x+5))}}}


{{{x(x+5)*((x+4)/(x+5)) = x(x+5)*((x-3)/x) + x(x+5)*((2x-7)/(x+5))}}}


{{{x*highlight((x+5))*((x+4)/(highlight(x+5))) = highlight(x)*(x+5)*((x-3)/highlight(x)) + x*highlight((x+5))*((2x-7)/(highlight(x+5)))}}}


{{{x*cross((x+5))*((x+4)/(cross(x+5))) = cross(x)*(x+5)*((x-3)/cross(x)) + x*cross((x+5))*((2x-7)/(cross(x+5)))}}}


{{{x(x+4) = (x+5)*(x-3) + x(2x-7)}}}


Then let's expand everything out and get everything to one side.
{{{x(x+4) = (x+5)*(x-3) + x(2x-7)}}}


{{{x^2+4x = (x^2-3x+5x-15) + (2x^2-7x)}}}


{{{x^2+4x = 3x^2-5x-15}}}


{{{0 = 3x^2-5x-15-x^2-4x}}}


{{{0 = 2x^2-9x-15}}}


{{{2x^2-9x-15 = 0}}}


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Compare that to {{{ax^2+bx+c = 0}}}
a = 2, b = -9, c = -15


Plug those into the quadratic formula.
{{{x = (-b+-sqrt(b^2-4ac))/(2a)}}}


{{{x = (-(-9)+-sqrt((-9)^2-4(2)(-15)))/(2(2))}}}


{{{x = (9+-sqrt(81 + 120))/(4)}}}


{{{x = (9+-sqrt(201))/(4)}}}


{{{x = (9+sqrt(201))/(4) = 5.79436}}} or {{{x = (9-sqrt(201))/(4)=-1.29436}}}
Those are the two solutions.
The decimal values are approximate.
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