Solve 9a^2-(a+7^2/4a^2+7a

$$\frac{ 9 { a }^{ 2 } -(a+ { 7 }^{ 2 } }{ 4 { a }^{ 2 } +7a }$$

Evaluate

$$\frac{36a^{4}+63a^{3}-a-49}{a\left(4a+7\right)}$$

Short Solution Steps

Calculate 7 to the power of 2 and get 49.

$$9a^{2}-\frac{a+49}{4a^{2}+7a}$$

Factor 4a^{2}+7a.

$$9a^{2}-\frac{a+49}{a\left(4a+7\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 9a^{2} times \frac{a\left(4a+7\right)}{a\left(4a+7\right)}.

$$\frac{9a^{2}a\left(4a+7\right)}{a\left(4a+7\right)}-\frac{a+49}{a\left(4a+7\right)}$$

Since \frac{9a^{2}a\left(4a+7\right)}{a\left(4a+7\right)} and \frac{a+49}{a\left(4a+7\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9a^{2}a\left(4a+7\right)-\left(a+49\right)}{a\left(4a+7\right)}$$

Do the multiplications in 9a^{2}a\left(4a+7\right)-\left(a+49\right).

$$\frac{36a^{4}+63a^{3}-a-49}{a\left(4a+7\right)}$$

Expand a\left(4a+7\right).

$$\frac{36a^{4}+63a^{3}-a-49}{4a^{2}+7a}$$

Expand

$$\frac{36a^{4}+63a^{3}-a-49}{4a^{2}+7a}$$

Short Solution Steps

Calculate 7 to the power of 2 and get 49.

$$9a^{2}-\frac{a+49}{4a^{2}+7a}$$

Factor 4a^{2}+7a.

$$9a^{2}-\frac{a+49}{a\left(4a+7\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 9a^{2} times \frac{a\left(4a+7\right)}{a\left(4a+7\right)}.

$$\frac{9a^{2}a\left(4a+7\right)}{a\left(4a+7\right)}-\frac{a+49}{a\left(4a+7\right)}$$

Since \frac{9a^{2}a\left(4a+7\right)}{a\left(4a+7\right)} and \frac{a+49}{a\left(4a+7\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9a^{2}a\left(4a+7\right)-\left(a+49\right)}{a\left(4a+7\right)}$$

Do the multiplications in 9a^{2}a\left(4a+7\right)-\left(a+49\right).

$$\frac{36a^{4}+63a^{3}-a-49}{a\left(4a+7\right)}$$

Expand a\left(4a+7\right).

$$\frac{36a^{4}+63a^{3}-a-49}{4a^{2}+7a}$$