## Solving Rational Equations by Getting LCD

In the first video, we are going to solve rational equations by getting the LCD (Least Common Denominator).

**For Example:**

Find the LCD, which is . Multiple each expression to get its denominator to

Multiply

Now that the denominators are the same, we can add across

Solve the equation for the value of *x*. Combine like terms

Move *x* to one side of the equation

Isolate *x* and we have

## Solving Rational Equations by Multiplying by LCD

In the second video, we are going to solve rational equations by multiplying by the LCD (Least Common Denominator).

**For example:**

Determine the LCD of the three denominators, which is *2(x-6)(x+4)*. Multiply the numerators by the LCD

Reduce each expression

Multiply

Use the distributive property

Combine like terms

Move *x* to one side of the equation by subtracting *x*

Subtract *8* from both sides to isolate *x*, and we have

## Solving Rational Equations by using the Quadratic Formula

In the third video, we are going to solve rational equations by using the quadratic formula.

**For example:**

Determine the LCD, which is , and multiply it with each numerator

Reduce each expressions

Use the distributive property

Combine like terms

Subtract *3* from both sides of the equation so that it is equal to *0*

Divide by *3*

Use the quadratic formula to find x. First, identify the values of *a*, *b*, and *c*

Substitute the values into the quadratic formula and solve

Solve

*x* is and , so the solution set is

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