Solve for all values of x. (x+6)/(x-4)=(1)/(x) Answer: x=

Cross-multiply fractions: Cross-multiply to eliminate the fractions. (x + 6) * (x) = (1) * (x - 4)Distribute and simplify: Distribute to simplify both sides of the equation. x^2 + 6x = x - 4Bring terms together: Bring all terms to one side to set the equation to zero. x^2 + 6x - x + 4 = 0 x^2 + 5x + 4 = 0Factor quadratic equation: Factor the quadratic equation. (x + 4)(x + 1) = 0Set factors equal: Set each factor equal to zero and solve for x. x + 4 = 0 or x + 1 = 0 x = -4 or x = -1Check for extraneous solutions: Check for extraneous solutions by plugging the values back into the original equation. For x = -4: (-4 + 6) / (-4 - 4) = 1 / (-4) 2 / (-8) = -1/4 -1/4 = -1/4 (Valid solution) For x = -1: (-1 + 6) / (-1 - 4) = 1 / (-1) 5 / (-5) = -1 -1 = -1 (Valid solution)

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve for all values of
x.

(x+6)/(x-4)=(1)/(x)
Answer:
x=

Solve for all values of $x$ . $\newline$ $\frac{x+6}{x-4}=\frac{1}{x}$ $\newline$ Answer: $x=$

View step-by-step help

Home

Math Problems

Algebra 1

Solve multi-step linear equations

Full solution

Q. Solve for all values of

x

\newline

\frac{x+6}{x-4}=\frac{1}{x}

\newline

Answer:

x=

Cross-multiply fractions: Cross-multiply to eliminate the fractions. $\newline$ $(x + 6) \times (x) = (1) \times (x - 4)$
Distribute and simplify: Distribute to simplify both sides of the equation. $x^2 + 6x = x - 4$
Bring terms together: Bring all terms to one side to set the equation to zero. $\newline$ $x^2 + 6x - x + 4 = 0$ $\newline$ $x^2 + 5x + 4 = 0$
Factor quadratic equation: Factor the quadratic equation. $\newline$ $(x + 4)(x + 1) = 0$
Set factors equal: Set each factor equal to zero and solve for $x$ . $x + 4 = 0$ or $x + 1 = 0$ $x = -4$ or $x = -1$
Check for extraneous solutions: Check for extraneous solutions by plugging the values back into the original equation. $\newline$ For $x = -4$ : $\newline$ $(-4 + 6) / (-4 - 4) = 1 / (-4)$ $\newline$ $2 / (-8) = -1/4$ $\newline$ $-1/4 = -1/4$ (Valid solution) $\newline$ For $x = -1$ : $\newline$ $(-1 + 6) / (-1 - 4) = 1 / (-1)$ $\newline$ $5 / (-5) = -1$ $\newline$ $-1 = -1$ (Valid solution)