Solve -100+34/x+32*5/x^2+31*37/x^3+30*53/x^4+frac{27*9}{x^5}=

$$- 100 + \frac { 34 } { x } + \frac { 32 \cdot 5 } { x ^ { 2 } } + \frac { 31 \cdot 37 } { x ^ { 3 } } + \frac { 30 \cdot 53 } { x ^ { 4 } } + \frac { 27 \cdot 9 } { x ^ { 5 } } =$$

Evaluate

$$-100+\frac{34}{x}+\frac{160}{x^{2}}+\frac{1147}{x^{3}}+\frac{1590}{x^{4}}+\frac{243}{x^{5}}$$

Short Solution Steps

Multiply 32 and 5 to get 160.

$$-100+\frac{34}{x}+\frac{160}{x^{2}}+\frac{31\times 37}{x^{3}}+\frac{30\times 53}{x^{4}}+\frac{27\times 9}{x^{5}}$$

Multiply 31 and 37 to get 1147.

$$-100+\frac{34}{x}+\frac{160}{x^{2}}+\frac{1147}{x^{3}}+\frac{30\times 53}{x^{4}}+\frac{27\times 9}{x^{5}}$$

Multiply 30 and 53 to get 1590.

$$-100+\frac{34}{x}+\frac{160}{x^{2}}+\frac{1147}{x^{3}}+\frac{1590}{x^{4}}+\frac{27\times 9}{x^{5}}$$

Multiply 27 and 9 to get 243.

$$-100+\frac{34}{x}+\frac{160}{x^{2}}+\frac{1147}{x^{3}}+\frac{1590}{x^{4}}+\frac{243}{x^{5}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -100 times \frac{x}{x}.

$$-\frac{100x}{x}+\frac{34}{x}+\frac{160}{x^{2}}+\frac{1147}{x^{3}}+\frac{1590}{x^{4}}+\frac{243}{x^{5}}$$

Since -\frac{100x}{x} and \frac{34}{x} have the same denominator, add them by adding their numerators.

$$\frac{-100x+34}{x}+\frac{160}{x^{2}}+\frac{1147}{x^{3}}+\frac{1590}{x^{4}}+\frac{243}{x^{5}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x^{2} is x^{2}. Multiply \frac{-100x+34}{x} times \frac{x}{x}.

$$\frac{\left(-100x+34\right)x}{x^{2}}+\frac{160}{x^{2}}+\frac{1147}{x^{3}}+\frac{1590}{x^{4}}+\frac{243}{x^{5}}$$

Since \frac{\left(-100x+34\right)x}{x^{2}} and \frac{160}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(-100x+34\right)x+160}{x^{2}}+\frac{1147}{x^{3}}+\frac{1590}{x^{4}}+\frac{243}{x^{5}}$$

Do the multiplications in \left(-100x+34\right)x+160.

$$\frac{-100x^{2}+34x+160}{x^{2}}+\frac{1147}{x^{3}}+\frac{1590}{x^{4}}+\frac{243}{x^{5}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x^{2} and x^{3} is x^{3}. Multiply \frac{-100x^{2}+34x+160}{x^{2}} times \frac{x}{x}.

$$\frac{\left(-100x^{2}+34x+160\right)x}{x^{3}}+\frac{1147}{x^{3}}+\frac{1590}{x^{4}}+\frac{243}{x^{5}}$$

Since \frac{\left(-100x^{2}+34x+160\right)x}{x^{3}} and \frac{1147}{x^{3}} have the same denominator, add them by adding their numerators.

$$\frac{\left(-100x^{2}+34x+160\right)x+1147}{x^{3}}+\frac{1590}{x^{4}}+\frac{243}{x^{5}}$$

Do the multiplications in \left(-100x^{2}+34x+160\right)x+1147.

$$\frac{-100x^{3}+34x^{2}+160x+1147}{x^{3}}+\frac{1590}{x^{4}}+\frac{243}{x^{5}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x^{3} and x^{4} is x^{4}. Multiply \frac{-100x^{3}+34x^{2}+160x+1147}{x^{3}} times \frac{x}{x}.

$$\frac{\left(-100x^{3}+34x^{2}+160x+1147\right)x}{x^{4}}+\frac{1590}{x^{4}}+\frac{243}{x^{5}}$$

Since \frac{\left(-100x^{3}+34x^{2}+160x+1147\right)x}{x^{4}} and \frac{1590}{x^{4}} have the same denominator, add them by adding their numerators.

$$\frac{\left(-100x^{3}+34x^{2}+160x+1147\right)x+1590}{x^{4}}+\frac{243}{x^{5}}$$

Do the multiplications in \left(-100x^{3}+34x^{2}+160x+1147\right)x+1590.

$$\frac{-100x^{4}+34x^{3}+160x^{2}+1147x+1590}{x^{4}}+\frac{243}{x^{5}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x^{4} and x^{5} is x^{5}. Multiply \frac{-100x^{4}+34x^{3}+160x^{2}+1147x+1590}{x^{4}} times \frac{x}{x}.

$$\frac{\left(-100x^{4}+34x^{3}+160x^{2}+1147x+1590\right)x}{x^{5}}+\frac{243}{x^{5}}$$

Since \frac{\left(-100x^{4}+34x^{3}+160x^{2}+1147x+1590\right)x}{x^{5}} and \frac{243}{x^{5}} have the same denominator, add them by adding their numerators.

$$\frac{\left(-100x^{4}+34x^{3}+160x^{2}+1147x+1590\right)x+243}{x^{5}}$$

Do the multiplications in \left(-100x^{4}+34x^{3}+160x^{2}+1147x+1590\right)x+243.

$$\frac{-100x^{5}+34x^{4}+160x^{3}+1147x^{2}+1590x+243}{x^{5}}$$

Factor

$$-\frac{100x^{5}-34x^{4}-160x^{3}-1147x^{2}-1590x-243}{x^{5}}$$