Simplify: 3x-(3840 )/(x)=24

Isolate x in denominator: Step 1: Isolate the term with x in the denominator. Move 3x to the right side of the equation: - (3840/x) = 24 - 3xClear denominator by multiplying: Step 2: Multiply every term by x to clear the denominator. x * (-3840/x) = (24 - 3x) * x -3840 = 24x - 3x^2Rearrange to form quadratic equation: Step 3: Rearrange the equation to form a quadratic equation. 3x^2 - 24x - 3840 = 0Simplify quadratic equation: Step 4: Simplify the quadratic equation by dividing all terms by 3. x^2 - 8x - 1280 = 0Factorize quadratic equation: Step 5: Factorize the quadratic equation. (x - 40)(x + 32) = 0Solve for x: Step 6: Solve for x by setting each factor equal to zero. x - 40 = 0 or x + 32 = 0 x = 40 or x = -32

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Simplify: $3x-$ $\frac{3840}{x}$ = $24$

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Algebra 2

Simplify rational expressions

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Q. Simplify:

3x-

\frac{3840}{x}

24

Isolate x in denominator: Step $1$ : Isolate the term with x in the denominator. $\newline$ Move $3x$ to the right side of the equation: $\newline$ $- \frac{3840}{x} = 24 - 3x$
Clear denominator by multiplying: Step $2$ : Multiply every term by $x$ to clear the denominator. $x \cdot \left(-\frac{3840}{x}\right) = (24 - 3x) \cdot x$ $-3840 = 24x - 3x^2$
Rearrange to form quadratic equation: Step $3$ : Rearrange the equation to form a quadratic equation. $\newline$ $3x^2 - 24x - 3840 = 0$
Simplify quadratic equation: Step $4$ : Simplify the quadratic equation by dividing all terms by $3$ . $x^2 - 8x - 1280 = 0$
Factorize quadratic equation: Step $5$ : Factorize the quadratic equation. $\newline$ $(x - 40)(x + 32) = 0$
Solve for x: Step $6$ : Solve for x by setting each factor equal to zero. $\newline$ $x - 40 = 0$ or $x + 32 = 0$ $\newline$ $x = 40$ or $x = -32$