Solve f(x)=(2x+3)((3)/(x)-3) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$f(x)=(2x+3)( \frac{ 3 }{ x } -3)$$

Evaluate

$-6x-3+\frac{9}{x}$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply $3$ times $\frac{x}{x}$.

$$\left(2x+3\right)\left(\frac{3}{x}-\frac{3x}{x}\right)$$

Since $\frac{3}{x}$ and $\frac{3x}{x}$ have the same denominator, subtract them by subtracting their numerators.

$$\left(2x+3\right)\times \frac{3-3x}{x}$$

Express $\left(2x+3\right)\times \frac{3-3x}{x}$ as a single fraction.

$$\frac{\left(2x+3\right)\left(3-3x\right)}{x}$$

Apply the distributive property by multiplying each term of $2x+3$ by each term of $3-3x$.

$$\frac{6x-6x^{2}+9-9x}{x}$$

Combine $6x$ and $-9x$ to get $-3x$.

$$\frac{-3x-6x^{2}+9}{x}$$

Expand

$-6x-3+\frac{9}{x}$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply $3$ times $\frac{x}{x}$.

$$\left(2x+3\right)\left(\frac{3}{x}-\frac{3x}{x}\right)$$

Since $\frac{3}{x}$ and $\frac{3x}{x}$ have the same denominator, subtract them by subtracting their numerators.

$$\left(2x+3\right)\times \frac{3-3x}{x}$$

Express $\left(2x+3\right)\times \frac{3-3x}{x}$ as a single fraction.

$$\frac{\left(2x+3\right)\left(3-3x\right)}{x}$$

Apply the distributive property by multiplying each term of $2x+3$ by each term of $3-3x$.

$$\frac{6x-6x^{2}+9-9x}{x}$$

Combine $6x$ and $-9x$ to get $-3x$.

$$\frac{-3x-6x^{2}+9}{x}$$