How do you solve #\frac { x + 4} { x - 3} = \frac { x + 2} { x - 4}#?

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Answer 1 · 2017-03-25T09:18:57

#"The answer of your question is x=10"#

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

#"please note that : "a/b=c/d" than "a*d=b*c#

#"we can write the equation above as "#

#(x+4)(x-4)=(x-3)(x+2)#

#"Since "(x-y)(x+y)=x^2-y^2," we can write as the fallowing "#

#(x+4)(x-4)=x^2-4^2#

#x^2-4^2=(x-3)(x+2)#

#x^2-16=x^2+2x-3x-6#

#x^2-16=x^2-x-6#

#cancel(x^2)-16-cancel(x^2)+x+6=0#

#x-16+6=0#

#x-10=0#

#x=10#