Basic Math Examples

$\frac{5}{y^{2} - 3 y + 2} + \frac{1}{y - 2}$

Step 1

Factor $y^{2} - 3 y + 2$ using the AC method.

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Step 1.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $2$ and whose sum is $- 3$ .

$- 2, - 1$

Step 1.2

Write the factored form using these integers.

$\frac{5}{(y - 2) (y - 1)} + \frac{1}{y - 2}$

Step 2

To write $\frac{1}{y - 2}$ as a fraction with a common denominator, multiply by $\frac{y - 1}{y - 1}$ .

$\frac{5}{(y - 2) (y - 1)} + \frac{1}{y - 2} \cdot \frac{y - 1}{y - 1}$

Step 3

Multiply $\frac{1}{y - 2}$ by $\frac{y - 1}{y - 1}$ .

$\frac{5}{(y - 2) (y - 1)} + \frac{y - 1}{(y - 2) (y - 1)}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 + y - 1}{(y - 2) (y - 1)}$

Step 5

Subtract $1$ from $5$ .

$\frac{y + 4}{(y - 2) (y - 1)}$