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

## Example Questions

2

–1

1

0

–2

2

Explanation:

b/(m+ 1)

b/(m– 1)

–b/(+ 1)

–bm/(m+ 1)

bm/(m+ 1)

b/(m+ 1)

Explanation:

### Example Question #3 : How To Find The Solution To A Rational Equation With Lcd

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

Explanation:

### Example Question #101 : Algebra

Solve for x:

Explanation:

The first step is to cancel out the denominator by multiplying both sides by 7:

Subtract 3 from both sides to get  by itself:

### Example Question #106 : Algebra

Solve for  and  using elimination:

and

and

and

and

and

and

Explanation:

When using elimination, you need two factors to cancel out when the two equations are added together. We can get the  in the first equation to cancel out with the  in the second equation by multiplying everything in the second equation by :

Now our two equations look like this:

The  can cancel with the , giving us:

These equations, when summed, give us:

Once we know the value for , we can just plug it into one of our original equations to solve for the value of :

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

Give the solution set of the rational equation

Explanation:

Multiply both sides of the equation by the denominator :

Rewrite both expression using the binomial square pattern:

This can be rewritten as a linear equation by subtracting  from both sides:

Solve as a linear equation:

Solve: