Question 77029
{{{(5x-8)/(x+2)=(5x-1)/(x+3)}}} Start with the given problem

{{{(cross((x+2))(x+3))((5x-8)/cross((x+2)))=((5x-1)/cross((x+3)))((x+2)cross((x+3)))}}} Multiply by the LCD

{{{(5x-8)(x+3)=(5x-1)(x+2)}}}

{{{5x^2+15x-8x-24=5x^2+10x-x-2}}} foil the parenthesis

{{{5x^2+7x-24=5x^2+9x-2}}} Combine like terms

{{{7x-24=9x-2}}} Subtract {{{5x^2}}} from both sides

{{{-24=9x-7x-2}}} Subtract 7x from both sides

{{{-24+2=2x}}} Add 2 to both sides

{{{-22=2x}}} 

{{{x=-22/2}}} Divide both sides by 2

{{{x=-11}}}

So {{{x=-11}}}

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Check:

{{{(5(-11)-8)/((-11)+2)=(5(-11)-1)/((-11)+3)}}} Plug in x=-11

{{{(-55-8)/(-9)=(-55-1)/(-8)}}}

{{{(-63)/(-9)=(-56)/(-8)}}}

{{{7=7}}} works