Solve y(x)=left(3/x^3+4/x^4right)left(x+1/x^4right)

$$y(x) = \left( \frac{ 3 }{ { x }^{ 3 } } + \frac{ 4 }{ { x }^{ 4 } } \right) \left( x+ \frac{ 1 }{ { x }^{ 4 } } \right)$$

Evaluate

$$\frac{\left(3x+4\right)\left(x^{5}+1\right)}{x^{8}}$$

Short Solution Steps

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{3}{x^{3}} times \frac{x}{x}.

$$\left(\frac{3x}{x^{4}}+\frac{4}{x^{4}}\right)\left(x+\frac{1}{x^{4}}\right)$$

Since \frac{3x}{x^{4}} and \frac{4}{x^{4}} have the same denominator, add them by adding their numerators.

$$\frac{3x+4}{x^{4}}\left(x+\frac{1}{x^{4}}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x^{4}}{x^{4}}.

$$\frac{3x+4}{x^{4}}\left(\frac{xx^{4}}{x^{4}}+\frac{1}{x^{4}}\right)$$

Since \frac{xx^{4}}{x^{4}} and \frac{1}{x^{4}} have the same denominator, add them by adding their numerators.

$$\frac{3x+4}{x^{4}}\times \frac{xx^{4}+1}{x^{4}}$$

Do the multiplications in xx^{4}+1.

$$\frac{3x+4}{x^{4}}\times \frac{x^{5}+1}{x^{4}}$$

Multiply \frac{3x+4}{x^{4}} times \frac{x^{5}+1}{x^{4}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(3x+4\right)\left(x^{5}+1\right)}{x^{4}x^{4}}$$

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$\frac{\left(3x+4\right)\left(x^{5}+1\right)}{x^{8}}$$

Use the distributive property to multiply 3x+4 by x^{5}+1.

$$\frac{3x^{6}+3x+4x^{5}+4}{x^{8}}$$

Expand

$$\frac{3x^{6}+4x^{5}+3x+4}{x^{8}}$$

Short Solution Steps

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{3}{x^{3}} times \frac{x}{x}.

$$\left(\frac{3x}{x^{4}}+\frac{4}{x^{4}}\right)\left(x+\frac{1}{x^{4}}\right)$$

Since \frac{3x}{x^{4}} and \frac{4}{x^{4}} have the same denominator, add them by adding their numerators.

$$\frac{3x+4}{x^{4}}\left(x+\frac{1}{x^{4}}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x^{4}}{x^{4}}.

$$\frac{3x+4}{x^{4}}\left(\frac{xx^{4}}{x^{4}}+\frac{1}{x^{4}}\right)$$

Since \frac{xx^{4}}{x^{4}} and \frac{1}{x^{4}} have the same denominator, add them by adding their numerators.

$$\frac{3x+4}{x^{4}}\times \frac{xx^{4}+1}{x^{4}}$$

Do the multiplications in xx^{4}+1.

$$\frac{3x+4}{x^{4}}\times \frac{x^{5}+1}{x^{4}}$$

Multiply \frac{3x+4}{x^{4}} times \frac{x^{5}+1}{x^{4}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(3x+4\right)\left(x^{5}+1\right)}{x^{4}x^{4}}$$

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$\frac{\left(3x+4\right)\left(x^{5}+1\right)}{x^{8}}$$

Use the distributive property to multiply 3x+4 by x^{5}+1.

$$\frac{3x^{6}+3x+4x^{5}+4}{x^{8}}$$