Solve 1/5x^2-y+5/4x-1/5x^2+y-3/2x-frac{11}{8}x^2+frac{3}{4}x

$$\frac{ 1 }{ 5 } { x }^{ 2 } -y+ \frac{ 5 }{ 4 } x- \frac{ 1 }{ 5 } { x }^{ 2 } +y- \frac{ 3 }{ 2 } x- \frac{ 11 }{ 8 } { x }^{ 2 } + \frac{ 3 }{ 4 } x$$

Evaluate

$$\frac{x\left(4-11x\right)}{8}$$

Solution Steps

Combine \frac{1}{5}x^{2} and -\frac{1}{5}x^{2} to get 0.

$$-y+\frac{5}{4}x+y-\frac{3}{2}x-\frac{11}{8}x^{2}+\frac{3}{4}x$$

Combine -y and y to get 0.

$$\frac{5}{4}x-\frac{3}{2}x-\frac{11}{8}x^{2}+\frac{3}{4}x$$

Combine \frac{5}{4}x and -\frac{3}{2}x to get -\frac{1}{4}x.

$$-\frac{1}{4}x-\frac{11}{8}x^{2}+\frac{3}{4}x$$

Combine -\frac{1}{4}x and \frac{3}{4}x to get \frac{1}{2}x.

$$\frac{1}{2}x-\frac{11}{8}x^{2}$$

Factor

$$\frac{x\left(4-11x\right)}{8}$$

Solution Steps

Factor out \frac{1}{40}.

$$\frac{8x^{2}-40y+50x-8x^{2}+40y-60x-55x^{2}+30x}{40}$$

Consider 8x^{2}-40y+50x-8x^{2}+40y-60x-55x^{2}+30x. Multiply and combine like terms.

$$-55x^{2}+20x$$

Consider -55x^{2}+20x. Factor out 5.

$$5\left(-11x^{2}+4x\right)$$

Consider -11x^{2}+4x. Factor out x.

$$x\left(-11x+4\right)$$

Rewrite the complete factored expression.

$$\frac{x\left(-11x+4\right)}{8}$$