(1)/(3x)+(1)/(2x)=(1)/(6)-(1)/(x)

Find Common Denominator: Find a common denominator for the fractions on the left side of the equation. The common denominator for 3x and 2x is 6x.Rewrite Fractions: Rewrite each fraction on the left side with the common denominator. (1)/(3x) becomes (2)/(6x) because (1 * 2)/(3x * 2) = (2)/(6x). (1)/(2x) becomes (3)/(6x) because (1 * 3)/(2x * 3) = (3)/(6x).Add Fractions: Add the fractions on the left side. (2)/(6x) + (3)/(6x) = (2 + 3)/(6x) = (5)/(6x).Rewrite Equation: Rewrite the equation with the combined fraction on the left side. (5)/(6x) = (1)/(6) - (1)/(x).Find Common Denominator: Find a common denominator for the fractions on the right side of the equation. The common denominator for 6 and x is 6x.Rewrite Fractions: Rewrite each fraction on the right side with the common denominator. (1)/(6) becomes (x)/(6x) because (1 * x)/(6 * x) = (x)/(6x). (1)/(x) becomes (6)/(6x) because (1 * 6)/(x * 6) = (6)/(6x).Subtract Fractions: Subtract the fractions on the right side. (x)/(6x) - (6)/(6x) = (x - 6)/(6x).Set Fractions Equal: Set the combined fractions from both sides equal to each other. (5)/(6x) = (x - 6)/(6x).Solve for x: Since the denominators are the same, we can set the numerators equal to each other. 5 = x - 6.Solve for x. Add 6 to both sides of the equation: 5 + 6 = x - 6 + 6. 11 = x.

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$\frac{1}{3 x}+\frac{1}{2 x}=\frac{1}{6}-\frac{1}{x}$

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Algebra 1

Multiplication with rational exponents

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\frac{1}{3 x}+\frac{1}{2 x}=\frac{1}{6}-\frac{1}{x}

Find Common Denominator: Find a common denominator for the fractions on the left side of the equation. $\newline$ The common denominator for $3x$ and $2x$ is $6x$ .
Rewrite Fractions: Rewrite each fraction on the left side with the common denominator. $\newline$ $(1)/(3x)$ becomes $(2)/(6x)$ because $(1 \times 2)/(3x \times 2) = (2)/(6x)$ . $\newline$ $(1)/(2x)$ becomes $(3)/(6x)$ because $(1 \times 3)/(2x \times 3) = (3)/(6x)$ .
Add Fractions: Add the fractions on the left side. $\newline$ $(\frac{2}{6x}) + (\frac{3}{6x}) = (\frac{2 + 3}{6x}) = (\frac{5}{6x})$ .
Rewrite Equation: Rewrite the equation with the combined fraction on the left side. $\newline$ rac{5}{6x} = rac{1}{6} - rac{1}{x}.
Find Common Denominator: Find a common denominator for the fractions on the right side of the equation. $\newline$ The common denominator for $6$ and $x$ is $6x$ .
Rewrite Fractions: Rewrite each fraction on the right side with the common denominator. $\newline$ $(1)/(6)$ becomes $(x)/(6x)$ because $(1 \times x)/(6 \times x) = (x)/(6x)$ . $\newline$ $(1)/(x)$ becomes $(6)/(6x)$ because $(1 \times 6)/(x \times 6) = (6)/(6x)$ .
Subtract Fractions: Subtract the fractions on the right side. $\frac{x}{6x} - \frac{6}{6x} = \frac{x - 6}{6x}$ .
Set Fractions Equal: Set the combined fractions from both sides equal to each other. $\frac{5}{6x} = \frac{x - 6}{6x}$ .
Solve for x: Since the denominators are the same, we can set the numerators equal to each other. $5 = x - 6$ .
Solve for x: Since the denominators are the same, we can set the numerators equal to each other. $\newline$ $5 = x - 6$ .Solve for x. $\newline$ Add $6$ to both sides of the equation: $5 + 6 = x - 6 + 6$ . $\newline$ $11 = x$ .