Solve -3x^2+5x+1/-2x^2+5x+1

$$\frac { - 3 x ^ { 2 } + 5 x + 1 } { - 2 x ^ { 2 } + 5 x + 1 }$$

Evaluate

$$\frac{1+5x-3x^{2}}{1+5x-2x^{2}}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{-3\left(x-\left(-\frac{1}{6}\sqrt{37}+\frac{5}{6}\right)\right)\left(x-\left(\frac{1}{6}\sqrt{37}+\frac{5}{6}\right)\right)}{-2\left(x-\left(-\frac{1}{4}\sqrt{33}+\frac{5}{4}\right)\right)\left(x-\left(\frac{1}{4}\sqrt{33}+\frac{5}{4}\right)\right)}$$

Cancel out -1 in both numerator and denominator.

$$\frac{3\left(x-\left(-\frac{1}{6}\sqrt{37}+\frac{5}{6}\right)\right)\left(x-\left(\frac{1}{6}\sqrt{37}+\frac{5}{6}\right)\right)}{2\left(x-\left(-\frac{1}{4}\sqrt{33}+\frac{5}{4}\right)\right)\left(x-\left(\frac{1}{4}\sqrt{33}+\frac{5}{4}\right)\right)}$$

Expand the expression.

$$\frac{3x^{2}-5x-1}{2x^{2}-5x-1}$$

Expand

$$\frac{1+5x-3x^{2}}{1+5x-2x^{2}}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{-3\left(x-\left(-\frac{1}{6}\sqrt{37}+\frac{5}{6}\right)\right)\left(x-\left(\frac{1}{6}\sqrt{37}+\frac{5}{6}\right)\right)}{-2\left(x-\left(-\frac{1}{4}\sqrt{33}+\frac{5}{4}\right)\right)\left(x-\left(\frac{1}{4}\sqrt{33}+\frac{5}{4}\right)\right)}$$

Cancel out -1 in both numerator and denominator.

$$\frac{3\left(x-\left(-\frac{1}{6}\sqrt{37}+\frac{5}{6}\right)\right)\left(x-\left(\frac{1}{6}\sqrt{37}+\frac{5}{6}\right)\right)}{2\left(x-\left(-\frac{1}{4}\sqrt{33}+\frac{5}{4}\right)\right)\left(x-\left(\frac{1}{4}\sqrt{33}+\frac{5}{4}\right)\right)}$$

Expand the expression.

$$\frac{3x^{2}-5x-1}{2x^{2}-5x-1}$$