Solve for z a^2+6a+5=(a+1)*z

$a^{2} + 6 a + 5 = (a + 1) \cdot z$

Step 1

Rewrite the equation as $(a + 1) \cdot z = a^{2} + 6 a + 5$ .

$(a + 1) \cdot z = a^{2} + 6 a + 5$

Step 2

Divide each term in $((a + 1) \cdot z) = a^{2} + 6 a + 5$ by $a + 1$ and simplify.

Divide each term in $((a + 1) \cdot z) = a^{2} + 6 a + 5$ by $a + 1$ .

$\frac{((a + 1) \cdot z)}{a + 1} = \frac{a^{2}}{a + 1} + \frac{6 a}{a + 1} + \frac{5}{a + 1}$

Simplify the left side.

Cancel the common factor of $a + 1$ .

Cancel the common factor.

$\frac{(a + 1) \cdot z}{a + 1} = \frac{a^{2}}{a + 1} + \frac{6 a}{a + 1} + \frac{5}{a + 1}$

Divide $z$ by $1$ .

$z = \frac{a^{2}}{a + 1} + \frac{6 a}{a + 1} + \frac{5}{a + 1}$

Simplify the right side.

Combine the numerators over the common denominator.

$z = \frac{a^{2} + 6 a + 5}{a + 1}$

Factor $a^{2} + 6 a + 5$ using the AC method.

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 $5$ and whose sum is $6$ .

$1, 5$

Write the factored form using these integers.

$z = \frac{(a + 1) (a + 5)}{a + 1}$

Cancel the common factor of $a + 1$ .

Cancel the common factor.

$z = \frac{(a + 1) (a + 5)}{a + 1}$

Divide $a + 5$ by $1$ .

$z = a + 5$

Solve for z a^2+6a+5=(a+1)*z

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