Subtract and Simplify \( \frac{5x}{3x^2} - \frac{7}{6x} \) - Math Solver AI

$Math Problem$

Mathematics High School

Question Content

Subtract and simplify \( \frac{5x}{3x^2} - \frac{7}{6x} \)

Correct Answer

A

Detailed Solution Steps

1
Find LCD of \( 3x^2 \) and \( 6x \): \( 6x^2 \)
2
Rewrite fractions with LCD: \( \frac{5x}{3x^2} = \frac{10x}{6x^2} \), \( \frac{7}{6x} = \frac{7x}{6x^2} \)
3
Subtract numerators: \( \frac{10x - 7x}{6x^2} = \frac{3x}{6x^2} \)
4
Simplify: \( \frac{3x}{6x^2} = \frac{1}{2x} \)

Knowledge Points Involved

1

Subtracting Rational Expressions

Requires finding a common denominator (LCD), rewriting fractions, then subtracting numerators.

2

Least Common Denominator (LCD)

The smallest expression that is a multiple of all denominators, found by LCM of coefficients and highest power of each variable.

3

Simplifying Rational Expressions

Reducing the fraction by canceling common factors in numerator and denominator.

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