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Adding and Subtracting Rational Expressions With Unlike
Denominators

Examples with Solutions

Example 1

We must have a common denominator before
we can add. The common denominator will be 10x^{ 2}

Now, we have to rename with a
denominator of 10x^{ 2}. To do this, we would
have to multiply 5x by 2x. If we multiply the denominator
by 2x we also have to multiply the numerator by 2x.

Now, we multiply before we add.

Now, we add since we have a common
denominator.

This is the final answer.

Example 2

First thing we do is to "add the
opposite" since this is subtraction.

We must have a common denominator before we can add.
The common denominator will be 12y^{ 3}

Now, we have to rename with a
denominator of 12y^{ 3} . To do this, we would
have to multiply 3y^{ 2} by 4y. If we multiply
the denominator by 4y we also have to multiply the
numerator by 4y.

Now, we multiply before we add.

Now, we add since we have a common
denominator.

This is the final answer.

Example 3

First thing we do is to "add the
opposite" since this is subtraction.

We must have a common denominator before we can add.
The only way to find the common denominator this time
will be to factor the first denominator.

The common denominator will be (a + 2) (a - 2).
Always use each factor the greater number of times it
appears in either factorization.

Now, we have to rename with a
denominator of (a + 2) (a - 2).

Now, we multiply before we add.

Now, we add since we have a common
denominator.

This is the final answer.

Example 4

We must have a common denominator before
we can add. The only way to find the common denominator
this time will be to factor the first denominator

The common denominator will be (y - 3) ( y + 2)
Always use each factor the greater number of times it
appears in either factorization.

Now, we have to rename with a
denominator of (y - 3) ( y + 2).