# ACT Math : How to find the solution to a rational equation with LCD

## Example Questions

### Example Question #1 : How To Find The Solution To A Rational Equation With Lcd

John, Jill, and Jack are splitting a pizza. John eats  of the pizza and Jill eats  of the pizza. How much of the pizza is left for Jack?

Explanation:

We can write an equation for the amount of pizza eaten, with  as the amount left for Jack.

To solve this equation, we must find the lowest common denominator of  and . We can list the multiples of  and  to find the least common multiple:

We can see that the least common multiple of  and  is , so we can rewrite each of the fractions with a denominator of .

When we put these fractions back into the equation, we can solve for :

### Example Question #1 : How To Find The Solution To A Rational Equation With Lcd

What is the slope of a line represented by the equation:

Explanation:

To solve problems where you need to find the slope of a line in a given equation, change the equation so that it matches y-intercept form:

For this equation, first move the 3x over to the other side of the equation.

The equation should now look like this:

Then, divide by 15 to isolate the variable .

Then simplify

Whatever number is before the x in the equation (m) is your slope.

0

1

–2

–1

2

2

Explanation:

–b/(+ 1)

bm/(m+ 1)

b/(m+ 1)

–bm/(m+ 1)

b/(m– 1)

b/(m+ 1)

Explanation:

### Example Question #101 : Linear / Rational / Variable Equations

In the equation below, , , and are non-zero numbers. What is the value of in terms of and ?