Solve for x. (1)/(5)-(5)/(x)=(-8)/(5x) Answer: x=

Find Common Denominator: Find a common denominator for the terms on the left side of the equation. The common denominator for 5 and x is 5x. We will rewrite each fraction with the common denominator 5x.Rewrite with Common Denominator: Rewrite the equation with the common denominator. (1/5) becomes (x/5x) and (5/x) becomes (25/5x). The equation now looks like this: (x/5x) - (25/5x) = (-8/5x)Combine Fractions: Combine the fractions on the left side of the equation. Since they have the same denominator, we can combine the numerators: (x - 25)/5x = (-8/5x)Equate Numerators: Since the denominators on both sides of the equation are the same, we can equate the numerators. x - 25 = -8Solve for x: Solve for x by adding 25 to both sides of the equation. x - 25 + 25 = -8 + 25 x = 17

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Precalculus

Find the roots of factored polynomials

Full solution

Q. Solve for

x

\newline

\frac{1}{5}-\frac{5}{x}=\frac{-8}{5 x}

\newline

Answer:

x=

Find Common Denominator: Find a common denominator for the terms on the left side of the equation. $\newline$ The common denominator for $5$ and $x$ is $5x$ . We will rewrite each fraction with the common denominator $5x$ .
Rewrite with Common Denominator: Rewrite the equation with the common denominator. $\newline$ $(\frac{1}{5})$ becomes $(\frac{x}{5x})$ and $(\frac{5}{x})$ becomes $(\frac{25}{5x})$ . The equation now looks like this: $\newline$ $(\frac{x}{5x}) - (\frac{25}{5x}) = (\frac{-8}{5x})$
Combine Fractions: Combine the fractions on the left side of the equation. $\newline$ Since they have the same denominator, we can combine the numerators: $\newline$ $(x - 25)/5x = (-8/5x)$
Equate Numerators: Since the denominators on both sides of the equation are the same, we can equate the numerators. $x - 25 = -8$
Solve for x: Solve for x by adding $25$ to both sides of the equation. $\newline$ $x - 25 + 25 = -8 + 25$ $\newline$ $x = 17$