Math / Algebra

QuestionQuestion 3 of 5
Subtract the following rational expressions $\frac{f+g}{16}-\frac{f-g}{16}$

Studdy Solution

STEP 1

1. The denominators of the rational expressions are the same.
2. The subtraction can be performed directly since the denominators are identical.
3. Simplification of the resulting expression is possible.

STEP 2

1. Subtract the numerators of the rational expressions.
2. Simplify the resulting expression.

STEP 3

Since the denominators are the same, subtract the numerators:
$\frac{f+g}{16} - \frac{f-g}{16} = \frac{(f+g) - (f-g)}{16}$

STEP 4

Simplify the expression in the numerator:
$(f+g) - (f-g) = f + g - f + g = 2g$

STEP 5

Now substitute back into the fraction:
$\frac{2g}{16}$
Simplify the fraction by dividing the numerator and the denominator by their greatest common divisor, which is 2:
$\frac{2g}{16} = \frac{g}{8}$
The simplified expression is:
$\boxed{\frac{g}{8}}$

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QuestionQuestion 3 of 5
Subtract the following rational expressions $\frac{f+g}{16}-\frac{f-g}{16}$

Studdy Solution

STEP 1

1. The denominators of the rational expressions are the same.
2. The subtraction can be performed directly since the denominators are identical.
3. Simplification of the resulting expression is possible.

STEP 2

1. Subtract the numerators of the rational expressions.
2. Simplify the resulting expression.

STEP 3

Since the denominators are the same, subtract the numerators:
$\frac{f+g}{16} - \frac{f-g}{16} = \frac{(f+g) - (f-g)}{16}$

STEP 4

Simplify the expression in the numerator:
$(f+g) - (f-g) = f + g - f + g = 2g$

STEP 5

Now substitute back into the fraction:
$\frac{2g}{16}$
Simplify the fraction by dividing the numerator and the denominator by their greatest common divisor, which is 2:
$\frac{2g}{16} = \frac{g}{8}$
The simplified expression is:
$\boxed{\frac{g}{8}}$

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QuestionQuestion 3 of 5Subtract the following rational expressions f+g16−f−g16\frac{f+g}{16}-\frac{f-g}{16}16f+g​−16f−g​

Studdy Solution

STEP 1

1. The denominators of the rational expressions are the same.2. The subtraction can be performed directly since the denominators are identical.3. Simplification of the resulting expression is possible.

STEP 2

1. Subtract the numerators of the rational expressions.2. Simplify the resulting expression.

STEP 3

Since the denominators are the same, subtract the numerators:f+g16−f−g16=(f+g)−(f−g)16 \frac{f+g}{16} - \frac{f-g}{16} = \frac{(f+g) - (f-g)}{16} 16f+g​−16f−g​=16(f+g)−(f−g)​

STEP 4

Simplify the expression in the numerator:(f+g)−(f−g)=f+g−f+g=2g (f+g) - (f-g) = f + g - f + g = 2g (f+g)−(f−g)=f+g−f+g=2g

STEP 5

Now substitute back into the fraction:2g16 \frac{2g}{16} 162g​Simplify the fraction by dividing the numerator and the denominator by their greatest common divisor, which is 2:2g16=g8 \frac{2g}{16} = \frac{g}{8} 162g​=8g​ The simplified expression is:g8 \boxed{\frac{g}{8}} 8g​​

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QuestionQuestion 3 of 5
Subtract the following rational expressions $\frac{f+g}{16}-\frac{f-g}{16}$

1. The denominators of the rational expressions are the same.
2. The subtraction can be performed directly since the denominators are identical.
3. Simplification of the resulting expression is possible.

1. Subtract the numerators of the rational expressions.
2. Simplify the resulting expression.

Since the denominators are the same, subtract the numerators:
$\frac{f+g}{16} - \frac{f-g}{16} = \frac{(f+g) - (f-g)}{16}$

Simplify the expression in the numerator:
$(f+g) - (f-g) = f + g - f + g = 2g$

Now substitute back into the fraction:
$\frac{2g}{16}$
Simplify the fraction by dividing the numerator and the denominator by their greatest common divisor, which is 2:
$\frac{2g}{16} = \frac{g}{8}$
The simplified expression is:
$\boxed{\frac{g}{8}}$