Adding and Subtracting Rational Expressions - Algebra 2

Multiply the denominators to get the least common denominator. We can then convert both fractions so that the denominators are alike.

Simplify both the top and the bottom.

Combine the numerators as one fraction. Be careful with the second fraction since the entire numerator is a quantity, which means we will need to brace with parentheses.

Pull out a common factor of negative one in the denominator. This allows us to rewrite the fraction with the negative sign in front of the fraction.

The answer is:

To simplify this expression, we will need to multiply both denominators together to find the least common denominator.

Convert both fractions to the common denominator.

Combine the fractions.

The answer is:

Evaluate by changing the denominator of the second fraction so that both fractions have similar denominators.

Use distribution to simplify the numerator.

Combine like-terms.

The answer is:

In order to subtract the fractions, we will need to determine the least common denominator.

Multiply the second fraction's numerator and denominator by ten, since both fractions share an x-term.

Combine the numerator to form one fraction.

The answer is:

In order to add the numerators, we will need to find the least common denominator.

Use the FOIL method to multiply the two denominators together.

Simplify by combining like-terms. The LCD is:

Change the fractions.

Simplify the fractions.

Combine like-terms.

The answer is:

Determine the least common denominator in order to add the numerator.

Each denominator shares an term. The least common denominator is since it is divisible by each coefficient of the denominator.

Convert the fractions.

Simplify the top and bottom.

The answer is:

In order to solve this expression, we will need to determine the least common denominator. Notice that the denominators both share an x term. We do not need to change that.

Multiply the denominator of the first fraction by two to get the least common denominator, which is .

Add the numerators.

The answer is:

Determine the least common denominator by multiplying the denominators together.

Convert the fractions given.

Simplify the numerators and denominators.

Combine the terms as one fraction. Make sure to brace the term since this is a quantity.

The answer is:

Identify the least common denominator by multiplying the denominators together.

Convert the fractions.

Simplify the numerator and denominator.

Combine both fractions as one. Make sure to enclose the second number in parentheses since the negative sign is distributive.

The answer is:

(x+5)(x+3) is the common denominator for this problem making the numerators 7(x+3) and 8(x+5).

7(x+3)+8(x+5)= 7x+21+8x+40= 15x+61

A=61

First, simplify the expression before attempting to combine like-terms.

Combine like-terms.

The values can only be added or subtracted if there are like-terms in the expression. Since there are no like-terms in the question, the question is already simplified as is. All the other answers given are incorrect.

Because the two rational expressions have the same denominator, we can simply add straight across the top. The denominator stays the same.

Therefore the answer is .

There are multiple operations required in this problem. The exponent must be eliminated before distributing the negative sign. Use the FOIL method which means to mulitply the first terms together, then multiply the outer terms together, then multiply the inner terms togethers, and lastly, mulitply the last terms together.

The negative sign can now be distributed.

First factor the denominators which gives us the following:

The two rational fractions have a common denominator hence they are like "like fractions". Hence we get:

Simplifying gives us

First let us find a common denominator as follows:

Now we can subtract the numerators which gives us :

So the final answer is

This is a more complicated form of

Find the least common denominator (LCD) and convert each fraction to the LCD, then add the numerators. Simplify as needed.

which is equivalent to

Simplify to get

With rational equations we must first note the domain, which is all real numbers except . (Recall, the denominator cannot equal zero. Thus, to find the domain set each denominator equal to zero and solve for what the variable cannot be.)

The least common denominator or and is . Multiply every term by the LCD to cancel out the denominators. The equation reduces to . We can FOIL to expand the equation to . Combine like terms and solve: . Factor the quadratic and set each factor equal to zero to obtain the solution, which is or . These answers are valid because they are in the domain.

a. Find a common denominator by identifying the Least Common Multiple of both denominators. The LCM of 3 and 1 is 3. The LCM of and is . Therefore, the common denominator is .

b. Write an equivialent fraction to using as the denominator. Multiply both the numerator and the denominator by to get . Notice that the second fraction in the original expression already has as a denominator, so it does not need to be converted.

The expression should now look like: .

c. Subtract the numerators, putting the difference over the common denominator.