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What is the least common denominator of the rational expressions below?
1/x^2 - 4/3x^2+15x

User Laalto
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2 Answers

12 votes

Answer:

The LCD is 3x²

The other two denominators can be factors of 3x²

Explanation:

To get the equivalent fractions, divide the original denominator into the LCD, then multiply the original numerator by the quotient.

For the first term: 1/x²

3x² ÷ x² = 3 3×1=3 The equivalent is 3/3x²

Second term: Leave it as it is.

For the third term: 15x

The implied denominator is 1

3x² ÷ 1 = 3x² 3x² × 15 = 135x²

The equivalent is 135x²/3x²

To check the validity, substitute a value for x and calculate the numbers.

For example let x = 3

The original expression becomes

1/3² + 4/3(3²) - 15(3)

1/9 + 4/27 - 45

With the LCD it is

3/27 + 4/27 - 1215/27

3 votes

Answer:

3x^2(x+5)

Explanation:

hope this helps

User Badaro
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