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Math 51

7.3/7.4 – Rational Expressions: LCD, Adding, and Subtracting

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The least common denominator (LCD) is the simplest expression that is divisible by all given denominators.

To find it, write the prime factorization of each denominator, and take the most number of each factor you see.

LCD

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The least common denominator (LCD) is the simplest expression that is divisible by all given denominators.

To find it, write the prime factorization of each denominator, and take the most number of each factor you see.

LCD

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Ex 1.Find the LCD of and .

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Ex 2.Find the LCD of and .

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Ex 3.Find the LCD of , , and

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Ex 4.Find the LCD of and .

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Ex 5.Rewrite the following rational expression with the indicated denominator.

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Ex 6.Rewrite the following rational expression with the indicated denominator.

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Ex 7.Rewrite the following rational expression with the indicated denominator.

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Ex 8.Rewrite the following rational expression with the indicated denominator.

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To add or subtract rational #’s with the same denominators, just add or subtract numerators:

ex:

With rational expressions, it’s the same.

Adding and Subtracting

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To add or subtract rational #’s with the same denominators, just add or subtract numerators:

ex:

With rational expressions, it’s the same.

Adding and Subtracting

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To add or subtract rational #’s with the same denominators, just add or subtract numerators:

ex:

With rational expressions, it’s the same.

Adding and Subtracting

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To add or subtract rational #’s with the same denominators, just add or subtract numerators:

ex:

With rational expressions, it’s the same.

Adding and Subtracting

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To add or subtract rational #’s with the same denominators, just add or subtract numerators:

ex:

With rational expressions, it’s the same.

Adding and Subtracting

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To add or subtract rational #’s with the same denominators, just add or subtract numerators:

ex:

With rational expressions, it’s the same.

Adding and Subtracting

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To add or subtract rational #’s with the same denominators, just add or subtract numerators:

ex:

With rational expressions, it’s the same.

Adding and Subtracting

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Ex 9.Add. Write each answer in lowest terms.

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Ex 10.Subtract. Write each answer in lowest terms.

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Recall: When adding and , we look for the _______, which is ___.

Then we write equivalent fractions for both and add:

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It’s similar for rational expressions.

Different Denominators

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Recall: When adding and , we look for the _______, which is ___.

Then we write equivalent fractions for both and add:

.

It’s similar for rational expressions.

Different Denominators

LCD

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Recall: When adding and , we look for the _______, which is ___.

Then we write equivalent fractions for both and add:

.

It’s similar for rational expressions.

Different Denominators

LCD 6

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Recall: When adding and , we look for the _______, which is ___.

Then we write equivalent fractions for both and add:

.

It’s similar for rational expressions.

Different Denominators

LCD 6

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Recall: When adding and , we look for the _______, which is ___.

Then we write equivalent fractions for both and add:

.

It’s similar for rational expressions.

Different Denominators

LCD 6

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Recall: When adding and , we look for the _______, which is ___.

Then we write equivalent fractions for both and add:

.

It’s similar for rational expressions.

Different Denominators

LCD 6

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Recall: When adding and , we look for the _______, which is ___.

Then we write equivalent fractions for both and add:

.

It’s similar for rational expressions.

Different Denominators

LCD 6

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Ex 11.Add. Write each answer in lowest terms.

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Ex 12.Subtract. Write each answer in lowest terms.

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Ex 13.Subtract. Write each answer in lowest terms.