Precalculus Examples

$g (f + g) (x) = 2 x - 3$

Step 1

Simplify $g (f + g) x$ .

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Step 1.1

Rewrite.

$0 + 0 + g (f + g) x = 2 x - 3$

Step 1.2

Simplify by adding zeros.

$g (f + g) x = 2 x - 3$

Step 1.3

Apply the distributive property.

$(g f + g \cdot g) x = 2 x - 3$

Step 1.4

Multiply $g$ by $g$ .

$(g f + g^{2}) x = 2 x - 3$

Step 1.5

Apply the distributive property.

$g f x + g^{2} x = 2 x - 3$

Step 2

Subtract $2 x$ from both sides of the equation.

$g f x + g^{2} x - 2 x = - 3$

Step 3

Factor $x$ out of $g f x + g^{2} x - 2 x$ .

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Step 3.1

Factor $x$ out of $g f x$ .

$x (g f) + g^{2} x - 2 x = - 3$

Step 3.2

Factor $x$ out of $g^{2} x$ .

$x (g f) + x g^{2} - 2 x = - 3$

Step 3.3

Factor $x$ out of $- 2 x$ .

$x (g f) + x g^{2} + x \cdot - 2 = - 3$

Step 3.4

Factor $x$ out of $x (g f) + x g^{2}$ .

$x (g f + g^{2}) + x \cdot - 2 = - 3$

Step 3.5

Factor $x$ out of $x (g f + g^{2}) + x \cdot - 2$ .

$x (g f + g^{2} - 2) = - 3$

Step 4

Divide each term in $x (g f + g^{2} - 2) = - 3$ by $g f + g^{2} - 2$ and simplify.

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Step 4.1

Divide each term in $x (g f + g^{2} - 2) = - 3$ by $g f + g^{2} - 2$ .

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $g f + g^{2} - 2$ .

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Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 3}{g f + g^{2} - 2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Move the negative in front of the fraction.

$x = - \frac{3}{g f + g^{2} - 2}$