How do you solve 7/(x+2)= 2/(x-5)7x+2=2x5?

1 Answer
May 2, 2016

x=39/5=7 4/5x=395=745

Explanation:

Given
color(white)("XXX")7/(x+2)=2/(x-5)color(white)("XXX")XXX7x+2=2x5XXXnote: this equation implies x!=-2x2 and x!=5x5

Multiply both sides by (x+2)(x-5)(x+2)(x5) (sometimes this will be called "cross multiplying")
color(white)("XXX")7(x-5)=2(x+2)XXX7(x5)=2(x+2)
simplify:
color(white)("XXX")7x-35=2x+4XXX7x35=2x+4
subtract 2x2x from both sides and add 3535 to both sides
color(white)("XXX")5x=39XXX5x=39
divide both sides by 55
color(white)("XXX")x=39/5XXXx=395