8. Write $$ \frac{3 x^{2}+6 x}{2 x y+4 y} imes \frac{2 y}{9 x^{2}} $$ in its simplified form and substitute the value to evaluate, given that $$ x=1 $$ and $$ y=2 $$.

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8. Write $$ \frac{3 x^{2}+6 x}{2 x y+4 y} 	imes \frac{2 y}{9 x^{2}} $$ in its simplified form and substitute the value to evaluate, given that $$ x=1 $$ and $$ y=2 $$.

UpStudy AI · Accepted Answer

Calculate or simplify the expression $$ (3*x^2+6*x)/(2*x*y+4*y) * (2*y)/(9*x^2) $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{\frac{\left(3x^{2}+6xight)}{\left(2xy+4yight)}	imes 2y}{9x^{2}}$$
- step1: Remove the parentheses:
  $$\frac{\frac{3x^{2}+6x}{2xy+4y}	imes 2y}{9x^{2}}$$
- step2: Divide the terms:
  $$\frac{\frac{3x}{2y}	imes 2y}{9x^{2}}$$
- step3: Multiply the terms:
  $$\frac{3x}{9x^{2}}$$
- step4: Simplify the expression:
  $$\frac{3}{9x^{2-1}}$$
- step5: Calculate:
  $$\frac{3}{9x}$$
- step6: Calculate:
  $$\frac{1}{3x}$$
The simplified form of the expression $$ \frac{3 x^{2}+6 x}{2 x y+4 y} 	imes \frac{2 y}{9 x^{2}} $$ is $$ \frac{1}{3x} $$.

Now, we need to substitute the values of $$ x=1 $$ and $$ y=2 $$ into the simplified expression to evaluate it.

Substituting $$ x=1 $$ and $$ y=2 $$ into the expression $$ \frac{1}{3x} $$, we get:

$$ \frac{1}{3(1)} = \frac{1}{3} $$

Therefore, the value of the expression when $$ x=1 $$ and $$ y=2 $$ is $$ \frac{1}{3} $$.
The simplified form of the expression is $$ \frac{1}{3x} $$. When $$ x=1 $$, the value is $$ \frac{1}{3} $$.

8. Write \( \frac{3 x^{2}+6 x}{2 x y+4 y} \times \frac{2 y}{9 x^{2}} \) in its simplified form and substitute the value to evaluate, given that \( x=1 \) and \( y=2 \).

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