Solve for all values of x. (x-3)/(x+2)=(4)/(x) Answer: x=

Find Common Denominator: First, we need to find a common denominator to combine the fractions on both sides of the equation. The common denominator for (x+2) and x is x(x+2).Multiply by Common Denominator: Next, we multiply both sides of the equation by the common denominator x(x+2) to eliminate the fractions: (x-3)/(x+2) * x(x+2) = (4)/(x) * x(x+2)Simplify Equation: Simplify the equation by canceling out the denominators: (x-3) * x = 4 * (x+2)Distribute Terms: Now, distribute the x on the left side and the 4 on the right side: x^2 - 3x = 4x + 8Combine Like Terms: Bring all terms to one side to set the equation to zero: x^2 - 3x - 4x - 8 = 0Factor Quadratic Equation: Combine like terms: x^2 - 7x - 8 = 0Set Factors Equal to Zero: Factor the quadratic equation: (x - 8)(x + 1) = 0Solve for x: Set each factor equal to zero and solve for x: x - 8 = 0 or x + 1 = 0Solve each equation for x: x = 8 or x = -1

Home

Math Problems

Precalculus

Find the roots of factored polynomials

Full solution

Q. Solve for all values of

x

\newline

\frac{x-3}{x+2}=\frac{4}{x}

\newline

Answer:

x=

Find Common Denominator: First, we need to find a common denominator to combine the fractions on both sides of the equation. The common denominator for $(x+2)$ and $x$ is $x(x+2)$ .
Multiply by Common Denominator: Next, we multiply both sides of the equation by the common denominator $x(x+2)$ to eliminate the fractions: $\frac{x-3}{x+2} \cdot x(x+2) = \frac{4}{x} \cdot x(x+2)$
Simplify Equation: Simplify the equation by canceling out the denominators: $(x-3) \times x = 4 \times (x+2)$
Distribute Terms: Now, distribute the $x$ on the left side and the $4$ on the right side: $x^2 - 3x = 4x + 8$
Combine Like Terms: Bring all terms to one side to set the equation to zero: $x^2 - 3x - 4x - 8 = 0$
Factor Quadratic Equation: Combine like terms: $x^2 - 7x - 8 = 0$
Set Factors Equal to Zero: Factor the quadratic equation: $\newline$ egin{equation}(x - $8$ )(x + $1$ ) = $0$ $\newline$ egin{equation}
Solve for $x$ : Set each factor equal to zero and solve for $x$ : $x - 8 = 0$ or $x + 1 = 0$
Solve for x: Set each factor equal to zero and solve for x: $\newline$ $x - 8 = 0$ or $x + 1 = 0$ Solve each equation for x: $\newline$ $x = 8$ or $x = -1$