Solving a Linear Fractional Equation

Hi Illianna, let's solve this rational equation together.

We start with the equation x plus ten over x minus seven equals eight over nine. To solve for x, we can use the cross-multiplication method.

Cross-multiplying means multiplying the numerator of one side by the denominator of the other side. This gives us nine times x plus ten equals eight times x minus seven.

Now, distribute the numbers on both sides. On the left, nine times x plus nine times ten gives us nine x plus ninety. On the right, eight times x minus eight times seven gives us eight x minus fifty-six.

Our next goal is to get all the x terms on one side. Let's subtract eight x from both sides.