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(3x)/(2b)-(5x)/(6b)
Which of the following expressions is equivalent to the given expression for
b!=0 ?

$\frac{3 x}{2 b}-\frac{5 x}{6 b}$ $\newline$ Which of the following expressions is equivalent to the given expression for $b \neq 0$ ?

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Simplify radical expressions with root inside the root

Full solution

Q.

\frac{3 x}{2 b}-\frac{5 x}{6 b}

\newline

Which of the following expressions is equivalent to the given expression for

b \neq 0

?

Find Common Denominator: To combine the two fractions, we need to find a common denominator. The denominators are $2b$ and $6b$ . The least common denominator (LCD) is $6b$ because $6b$ is the smallest number that both $2b$ and $6b$ can divide into without a remainder.
Rewrite Fractions: Now we need to rewrite each fraction with the common denominator of $6b$ . To do this, we multiply the numerator and denominator of the first fraction by $3$ , because $3 \times 2b = 6b$ . $\frac{3x}{2b} \times \frac{3}{3} = \frac{9x}{6b}$
Subtract Fractions: The second fraction already has the denominator $6b$ , so we do not need to change it. $\frac{5x}{6b}$ remains the same.
Combine Numerators: Now we subtract the two fractions with the common denominator. $(9x)/(6b) - (5x)/(6b)$
Perform Subtraction: Since the denominators are the same, we can subtract the numerators directly. $(9x - 5x)/(6b)$
Simplify Fraction: Perform the subtraction in the numerator. $\newline$ $(9x - 5x) = 4x$ $\newline$ So, the expression becomes $\frac{4x}{6b}$ .
Simplify Fraction: Perform the subtraction in the numerator. $\newline$ $(9x - 5x) = 4x$ $\newline$ So, the expression becomes $\frac{4x}{6b}$ .We can simplify the fraction $\frac{4x}{6b}$ by dividing both the numerator and the denominator by their greatest common divisor, which is $2$ . $\newline$ $\frac{4x}{2}$ / $\frac{6b}{2}$ = $\frac{2x}{3b}$

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