Simplify (10x+5z)/(14x^2+5xz-z^2)

$\frac{10 x + 5 z}{14 x^{2} + 5 x z - z^{2}}$

Step 1

Factor $5$ out of $10 x + 5 z$ .

Factor $5$ out of $10 x$ .

$\frac{5 (2 x) + 5 z}{14 x^{2} + 5 x z - z^{2}}$

Factor $5$ out of $5 z$ .

$\frac{5 (2 x) + 5 (z)}{14 x^{2} + 5 x z - z^{2}}$

Factor $5$ out of $5 (2 x) + 5 (z)$ .

$\frac{5 (2 x + z)}{14 x^{2} + 5 x z - z^{2}}$

Step 2

Simplify the denominator.

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 14 \cdot - 1 = - 14$ and whose sum is $b = 5$ .

Reorder terms.

$\frac{5 (2 x + z)}{14 x^{2} - z^{2} + 5 x z}$

Reorder $- z^{2}$ and $5 x z$ .

$\frac{5 (2 x + z)}{14 x^{2} + 5 x z - z^{2}}$

Factor $5$ out of $5 x z$ .

$\frac{5 (2 x + z)}{14 x^{2} + 5 (x z) - z^{2}}$

Rewrite $5$ as $- 2$ plus $7$

$\frac{5 (2 x + z)}{14 x^{2} + (- 2 + 7) (x z) - z^{2}}$

Apply the distributive property.

$\frac{5 (2 x + z)}{14 x^{2} - 2 (x z) + 7 (x z) - z^{2}}$

Move parentheses.

$\frac{5 (2 x + z)}{14 x^{2} - 2 x z + 7 x z - z^{2}}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{5 (2 x + z)}{(14 x^{2} - 2 x z) + 7 x z - z^{2}}$

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

$\frac{5 (2 x + z)}{2 x (7 x - 1 z) + z (7 x - z)}$

Factor the polynomial by factoring out the greatest common factor, $7 x - 1 z$ .

$\frac{5 (2 x + z)}{(7 x - 1 z) (2 x + z)}$

Rewrite $- 1 z$ as $- z$ .

$\frac{5 (2 x + z)}{(7 x - z) (2 x + z)}$

Step 3

Cancel the common factor of $2 x + z$ .

Cancel the common factor.

$\frac{5 (2 x + z)}{(7 x - z) (2 x + z)}$

Rewrite the expression.

$\frac{5}{7 x - z}$

Simplify (10x+5z)/(14x^2+5xz-z^2)

Related Questions

Support LCMGCF.com by disabling your adblocker.