Week 16 – solving rational equations

Solve: \frac{x}{x+3}=\frac{8}{x+6}

For solving, the first thing you want to do is make sure everything is in factored form.  Since this cannot be further factored, we can go to our next step which is to find the non-permissible values.  We cant have the denominator equal zero, therefore x cannot equal -3 or -6.  Now we can cross-multiply to get rid of the fraction and make it a lot easier to solve.

(x)(x+6)=(8)(x+3)

 

Distribute: x^2+6x=8x+24

 

Move everything to one side following the rules of algebra so that it is a quadratic that equals zero.

x^2-2x-24=0

Now we can factor to find the values of x and solve the equation.

(x-6)(x+4)=0

x=6           x=-4

 

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