Solve 3x-1/5+x^2*x^3+8x^2-9/x^4+2=

$$\frac { 3 x - 1 } { 5 + x ^ { 2 } } \cdot \frac { x ^ { 3 } + 8 x ^ { 2 } - 9 } { x ^ { 4 } + 2 } =$$

Evaluate

$$\frac{\left(3x-1\right)\left(x^{3}+8x^{2}-9\right)}{\left(x^{2}+5\right)\left(x^{4}+2\right)}$$

Short Solution Steps

Multiply \frac{3x-1}{5+x^{2}} times \frac{x^{3}+8x^{2}-9}{x^{4}+2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(3x-1\right)\left(x^{3}+8x^{2}-9\right)}{\left(5+x^{2}\right)\left(x^{4}+2\right)}$$

Use the distributive property to multiply 3x-1 by x^{3}+8x^{2}-9 and combine like terms.

$$\frac{3x^{4}+23x^{3}-27x-8x^{2}+9}{\left(5+x^{2}\right)\left(x^{4}+2\right)}$$

Use the distributive property to multiply 5+x^{2} by x^{4}+2.

$$\frac{3x^{4}+23x^{3}-27x-8x^{2}+9}{5x^{4}+10+x^{6}+2x^{2}}$$

Expand

$$\frac{3x^{4}+23x^{3}-8x^{2}-27x+9}{\left(x^{2}+5\right)\left(x^{4}+2\right)}$$

Short Solution Steps

Multiply \frac{3x-1}{5+x^{2}} times \frac{x^{3}+8x^{2}-9}{x^{4}+2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(3x-1\right)\left(x^{3}+8x^{2}-9\right)}{\left(5+x^{2}\right)\left(x^{4}+2\right)}$$

Use the distributive property to multiply 3x-1 by x^{3}+8x^{2}-9 and combine like terms.

$$\frac{3x^{4}+23x^{3}-27x-8x^{2}+9}{\left(5+x^{2}\right)\left(x^{4}+2\right)}$$

Use the distributive property to multiply 5+x^{2} by x^{4}+2.

$$\frac{3x^{4}+23x^{3}-27x-8x^{2}+9}{5x^{4}+10+x^{6}+2x^{2}}$$