Solve 45/6*55x^2-258963/4

$$\frac{ 45 }{ 6 \times 55 { x }^{ 2 } } - \frac{ 258963 }{ 4 }$$

Evaluate

$$-\frac{258963}{4}+\frac{3}{22x^{2}}$$

Short Solution Steps

Multiply 6 and 55 to get 330.

$$\frac{45}{330x^{2}}-\frac{258963}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 330x^{2} and 4 is 660x^{2}. Multiply \frac{45}{330x^{2}} times \frac{2}{2}. Multiply \frac{258963}{4} times \frac{165x^{2}}{165x^{2}}.

$$\frac{45\times 2}{660x^{2}}-\frac{258963\times 165x^{2}}{660x^{2}}$$

Since \frac{45\times 2}{660x^{2}} and \frac{258963\times 165x^{2}}{660x^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{45\times 2-258963\times 165x^{2}}{660x^{2}}$$

Do the multiplications in 45\times 2-258963\times 165x^{2}.

$$\frac{90-42728895x^{2}}{660x^{2}}$$

Factor the expressions that are not already factored in \frac{90-42728895x^{2}}{660x^{2}}.

$$\frac{45\left(-949531x^{2}+2\right)}{660x^{2}}$$

Cancel out 15 in both numerator and denominator.

$$\frac{3\left(-949531x^{2}+2\right)}{44x^{2}}$$

Use the distributive property to multiply 3 by -949531x^{2}+2.

$$\frac{-2848593x^{2}+6}{44x^{2}}$$

Factor

$$-\frac{\frac{3}{44}\left(949531x^{2}-2\right)}{x^{2}}$$