Basic Math Examples

$1 - \frac{y - 1}{a} - \frac{y}{a^{2}}$

Step 1

Combine into one fraction.

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Step 1.1

Write $1$ as a fraction with a common denominator.

$\frac{a}{a} - \frac{y - 1}{a} - \frac{y}{a^{2}}$

Step 1.2

Combine the numerators over the common denominator.

$\frac{a - (y - 1)}{a} - \frac{y}{a^{2}}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the distributive property.

$\frac{a - y - - 1}{a} - \frac{y}{a^{2}}$

Step 2.2

Multiply $- 1$ by $- 1$ .

$\frac{a - y + 1}{a} - \frac{y}{a^{2}}$

Step 3

To write $\frac{a - y + 1}{a}$ as a fraction with a common denominator, multiply by $\frac{a}{a}$ .

$\frac{a - y + 1}{a} \cdot \frac{a}{a} - \frac{y}{a^{2}}$

Step 4

Write each expression with a common denominator of $a^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{a - y + 1}{a}$ by $\frac{a}{a}$ .

$\frac{(a - y + 1) a}{a \cdot a} - \frac{y}{a^{2}}$

Step 4.2

Multiply $a$ by $a$ .

$\frac{(a - y + 1) a}{a^{2}} - \frac{y}{a^{2}}$

Step 5

Combine the numerators over the common denominator.

$\frac{(a - y + 1) a - y}{a^{2}}$

Step 6

Simplify the numerator.

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Step 6.1

Apply the distributive property.

$\frac{a \cdot a - y a + 1 a - y}{a^{2}}$

Step 6.2

Simplify.

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Step 6.2.1

Multiply $a$ by $a$ .

$\frac{a^{2} - y a + 1 a - y}{a^{2}}$

Step 6.2.2

Multiply $a$ by $1$ .

$\frac{a^{2} - y a + a - y}{a^{2}}$

Step 6.3

Rewrite $a^{2} - y a + a - y$ in a factored form.

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Step 6.3.1

Factor out the greatest common factor from each group.

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Step 6.3.1.1

Group the first two terms and the last two terms.

$\frac{(a^{2} - y a) + a - y}{a^{2}}$

Step 6.3.1.2

Factor out the greatest common factor (GCF) from each group.

$\frac{a (a - y) + 1 (a - y)}{a^{2}}$

Step 6.3.2

Factor the polynomial by factoring out the greatest common factor, $a - y$ .

$\frac{(a - y) (a + 1)}{a^{2}}$