Solve for x. (-1)/(6)+(x-3)/(x)=(7)/(6x) Answer: x=

Identify common denominator: First, let's identify the common denominator for the fractions on both sides of the equation. The common denominator is 6x.Multiply by common denominator: Now, we will multiply each term by the common denominator (6x) to clear the fractions: 6x * (-1/6) + 6x * ((x-3)/x) = 6x * (7/(6x))Simplify each term: Simplify each term: -1 * x + 6 * (x-3) = 7Distribute the 6: Distribute the 6 in the second term: -x + 6x - 18 = 7Combine like terms: Combine like terms: 5x - 18 = 7Add 18 to isolate: Add 18 to both sides to isolate the term with x: 5x = 7 + 18Simplify right side: Simplify the right side: 5x = 25Divide both sides: Divide both sides by 5 to solve for x: x = 25 / 5Simplify the division: Simplify the division: x = 5

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Math Problems

Precalculus

Find the roots of factored polynomials

Full solution

Q. Solve for

x

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\frac{-1}{6}+\frac{x-3}{x}=\frac{7}{6 x}

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Answer:

x=

Identify common denominator: First, let's identify the common denominator for the fractions on both sides of the equation. The common denominator is $6x$ .
Multiply by common denominator: Now, we will multiply each term by the common denominator $6x$ to clear the fractions: $\newline$ $6x \times (-\frac{1}{6}) + 6x \times (\frac{x-3}{x}) = 6x \times (\frac{7}{6x})$
Simplify each term: Simplify each term: $\newline$ $-1 \times x + 6 \times (x-3) = 7$
Distribute the $6$ : Distribute the $6$ in the second term: $-x + 6x - 18 = 7$
Combine like terms: Combine like terms: $5x - 18 = 7$
Add $18$ to isolate: Add $18$ to both sides to isolate the term with $x$ : $5x = 7 + 18$
Simplify right side: Simplify the right side: $5x = 25$
Divide both sides: Divide both sides by $5$ to solve for $x$ : $\newline$ $x = \frac{25}{5}$
Simplify the division: Simplify the division: $x = 5$