(x+5)/(5)=(6)/(x-2) Find x

Cross-multiply fractions: Cross-multiply to eliminate the fractions. (x + 5) * (x - 2) = 5 * 6Distribute and simplify: Distribute to simplify the left side of the equation. x(x - 2) + 5(x - 2) = 30 x^2 - 2x + 5x - 10 = 30Combine like terms: Combine like terms on the left side of the equation. x^2 + 3x - 10 = 30Move terms and set to zero: Move all terms to one side to set the equation to zero. x^2 + 3x - 10 - 30 = 0 x^2 + 3x - 40 = 0Factor quadratic equation: Factor the quadratic equation. (x + 8)(x - 5) = 0Set factors equal and solve: Set each factor equal to zero and solve for x. x + 8 = 0 or x - 5 = 0 x = -8 or x = 5Check solutions: Check the solutions in the original equation to ensure they do not create a division by zero or other inconsistencies. For x = -8: (-8 + 5)/5 = 6/(-8 - 2) -3/5 = 6/-10 -3/5 = -3/5 (This is consistent, so x = -8 is a valid solution.) For x = 5: (5 + 5)/5 = 6/(5 - 2) 10/5 = 6/3 2 = 2 (This is consistent, so x = 5 is also a valid solution.)

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Algebra 2

Add, subtract, multiply, and divide polynomials

Full solution

\frac{x+5}{5}=\frac{6}{x-2}

Find `x`

Cross-multiply fractions: Cross-multiply to eliminate the fractions. $\newline$ $(x + 5) \times (x - 2) = 5 \times 6$
Distribute and simplify: Distribute to simplify the left side of the equation. $\newline$ $x(x - 2) + 5(x - 2) = 30$ $\newline$ $x^2 - 2x + 5x - 10 = 30$
Combine like terms: Combine like terms on the left side of the equation. $x^2 + 3x - 10 = 30$
Move terms and set to zero: Move all terms to one side to set the equation to zero. $\newline$ $x^2 + 3x - 10 - 30 = 0$ $\newline$ $x^2 + 3x - 40 = 0$
Factor quadratic equation: Factor the quadratic equation. $\newline$ $(x + 8)(x - 5) = 0$
Set factors equal and solve: Set each factor equal to zero and solve for $x$ . $x + 8 = 0$ or $x - 5 = 0$ $x = -8$ or $x = 5$
Check solutions: Check the solutions in the original equation to ensure they do not create a division by zero or other inconsistencies. $\newline$ For $x = -8$ : $\newline$ $(-8 + 5)/5 = 6/(-8 - 2)$ $\newline$ $-3/5 = 6/-10$ $\newline$ $-3/5 = -3/5$ (This is consistent, so $x = -8$ is a valid solution.) $\newline$ For $x = 5$ : $\newline$ $(5 + 5)/5 = 6/(5 - 2)$ $\newline$ $10/5 = 6/3$ $\newline$ $2 = 2$ (This is consistent, so $x = 5$ is also a valid solution.)