# Algebra II : Solving Rational Expressions

## Example Questions

### Example Question #169 : Rational Expressions

Solve for .

Explanation:

To solve for the variable isolate it on one side of the equation by moving all other constants to the other side. To do this, perform opposite operations to manipulate the equation.

Cross multiply.

Remember we are multiplying  with the expression. Now distribute.

Divide  on both sides.

### Example Question #170 : Rational Expressions

Solve for .

Explanation:

To solve for the variable isolate it on one side of the equation by moving all other constants to the other side. To do this, perform opposite operations to manipulate the equation.

Cross multiply.

Remember we are multiplying  to the expression. Now distribute.

Divide  on both sides.

### Example Question #171 : Rational Expressions

Solve for .

Explanation:

To solve for the variable isolate it on one side of the equation by moving all other constants to the other side. To do this, perform opposite operations to manipulate the equation.

Cross multiply.

Remember to multiply  to each of the expressions respectively. Then distribute.

Subtract  and  on both sides.

### Example Question #172 : Rational Expressions

Solve for .

Explanation:

To solve for the variable isolate it on one side of the equation by moving all other constants to the other side. To do this, perform opposite operations to manipulate the equation.

Cross multiply.

Remember we are multiplying  to the expressions respectively. Then distribute.

Subtract  and  on both sides.

### Example Question #173 : Rational Expressions

Solve for .

Explanation:

To solve for the variable isolate it on one side of the equation by moving all other constants to the other side. To do this, perform opposite operations to manipulate the equation.

Cross multiply.

Remember we are multiplying  to the expression. Then we distribute.

Subtract  on both sides.

Divide  on both sides.

### Example Question #174 : Rational Expressions

Solve for .

Explanation:

To solve for the variable isolate it on one side of the equation by moving all other constants to the other side. To do this, perform opposite operations to manipulate the equation.

Distribute. Remember to apply FOIL.

Subtract  , , and  on both sides.

Divide  on both sides.

### Example Question #175 : Rational Expressions

Simplify:

Explanation:

To simplify the expressions, we will need a least common denominator.

Multiply the two denominators together to obtain the least common denominator.

Convert the fractions.

Combine the fractions as one fraction.

Simplify the numerator and combine like-terms.

### Example Question #176 : Rational Expressions

Explanation:

When considering the solution space for a rational function, we must look at the denominator.

Any value of x in the denominator that results in a zero cannot be part of the solution space because it is a mathematical impossibility to divide by 0.

(take the square root of both sides)

If we were to plug in a positive or negative 4 into the function, both of these would result in a zero in the denominator, which is a mathematical impossibility.

### Example Question #177 : Rational Expressions

Solve:

Explanation:

Convert the fractions to a common denominator.

Simplify the top and bottom and combine like terms on the numerator.

### Example Question #178 : Rational Expressions

Solve:

Explanation:

Find the least common denominator by multiplying both denominators together.

Convert the fractions.

Simplify the numerator and denominator.

Combine both fractions together.  Remember to brace the second numerator in parentheses.

Simplify the fraction.

Factor out a negative one in the denominator.