Solve frac{2(3x^{2})+3(2x^{2})+6x^2}{3x^2+5(2x^2)+7x^2}

$$\frac { 2 ( 3 x ^ { 2 } ) + 3 ( 2 x ^ { 2 } ) + 6 x ^ { 2 } } { 3 x ^ { 2 } + 5 ( 2 x ^ { 2 } ) + 7 x ^ { 2 } }$$

Evaluate

$$\frac{9}{10}=0.9$$

Solution Steps

Do the multiplications.

$$\frac{6x^{2}+6x^{2}+6x^{2}}{3x^{2}+5\times 2x^{2}+7x^{2}}$$

Combine 6x^{2} and 6x^{2} to get 12x^{2}.

$$\frac{12x^{2}+6x^{2}}{3x^{2}+5\times 2x^{2}+7x^{2}}$$

Combine 12x^{2} and 6x^{2} to get 18x^{2}.

$$\frac{18x^{2}}{3x^{2}+5\times 2x^{2}+7x^{2}}$$

Multiply 5 and 2 to get 10.

$$\frac{18x^{2}}{3x^{2}+10x^{2}+7x^{2}}$$

Combine 3x^{2} and 10x^{2} to get 13x^{2}.

$$\frac{18x^{2}}{13x^{2}+7x^{2}}$$

Combine 13x^{2} and 7x^{2} to get 20x^{2}.

$$\frac{18x^{2}}{20x^{2}}$$

Cancel out 2x^{2} in both numerator and denominator.

$$\frac{9}{10}$$

Factor

$$\frac{3 ^ {2}}{2 \cdot 5} = 0.9$$