What is (2y^2+4y)/(4z)*(12z^2)/(9y^2z+18yz) ?

The solution to (2y^2+4y)/(4z)*(12z^2)/(9y^2z+18yz) is 2/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (2y^2+4y)/(4z)*(12z^2)/(9y^2z+18yz)

simplify

\frac{2 y ^{2} + 4 y}{4 z} \cdot \frac{12 z ^{2}}{9 y ^{2} z + 18 yz}

\frac{2}{3}

Decimal Notation

0.66666 \dots

Solution steps

\frac{2 y ^{2} + 4 y}{4 z} \cdot \frac{12 z ^{2}}{9 y ^{2} z + 18 yz}

Cancel

\frac{2 y ^{2} + 4 y}{4 z} : \frac{y ( y + 2 )}{2 z}

= \frac{y ( y + 2 )}{2 z} \cdot \frac{12 z ^{2}}{9 y ^{2} z + 18 yz}

Cancel

\frac{12 z ^{2}}{9 y ^{2} z + 18 yz} : \frac{4 z}{3 y ( y + 2 )}

= \frac{y ( y + 2 )}{2 z} \cdot \frac{4 z}{3 y ( y + 2 )}

Apply the fraction rule:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{y ( y + 2 ) \cdot 4 z}{2 z \cdot 3 y ( y + 2 )}

Cancel the common factor:

y

= \frac{( y + 2 ) \cdot 4 z}{2 z \cdot 3 ( y + 2 )}

Cancel the common factor:

y + 2

= \frac{4 z}{2 z \cdot 3}

Cancel the common factor:

z

= \frac{4}{2 \cdot 3}

Factor the number:

4 = 2 \cdot 2

= \frac{2 \cdot 2}{2 \cdot 3}

Cancel the common factor:

2

= \frac{2}{3}

\frac{a - b}{3 a + 3 b} - \frac{a - 2 b}{6 a - 6 b} + \frac{a ^{2} + 2 ab - 6 b ^{2}}{9 a ^{2} - 9 b ^{2}}

(3 x + 2 y) (3 x + 2 y)

4 \cdot (- 9)

\frac{2}{2} + \frac{2}{3} + \frac{2}{4} + \frac{2}{5} + \frac{2}{6} + \frac{2}{7} + \frac{2}{8} + \frac{2}{9}

\frac{cot ( x )}{sin ( x )}

What is (2y^2+4y)/(4z)*(12z^2)/(9y^2z+18yz) ?
The solution to (2y^2+4y)/(4z)*(12z^2)/(9y^2z+18yz) is 2/3