Solving Rational Equations
x+4/5x+6 = 6/x+3

Solutions are x={1,-24} I think is what the lesson said, but I can't get to that point. I don't understand.

Question

Solving Rational Equations
x+4/5x+6 = 6/x+3

Solutions are x={1,-24} I think is what the lesson said, but I can't get to that point. I don't understand.

ganeshie8 · Answer

Have you tried cross multiplying ?

ganeshie8 · Answer

$$\large \dfrac{x+4}{5x+6} = \dfrac{6}{x+3}$$

implies

$$\large  (x+4)(x+3) = (6)(5x+6)$$

ganeshie8 · Answer

distribute and see what you can do

republican31 · Answer

$$x^2+7x+12=30x+36$$ Now what?

ganeshie8 · Answer

Perfect! 
collect like terms and make it look like a nice quadratic

ganeshie8 · Answer

subtract 30x both sides
then subtract 36 both sides

so that the right hand side becomes 0

republican31 · Answer

$$x^2-23x-24$$ Ok I see now thanks!

ganeshie8 · Answer

Np :) rest should be easy if you're familiar with solving quadratics

republican31 · Answer

Thank you so much I got it now!!!

ganeshie8 · Answer

glad to hear, yw !