Solve 10x^2-5x+8/5x^2+9x-19=2

$$\frac { 10 x ^ { 2 } - 5 x + 8 } { 5 x ^ { 2 } + 9 x - 19 } = 2$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5\left(x-\left(-\frac{1}{10}\sqrt{461}-\frac{9}{10}\right)\right)\left(x-\left(\frac{1}{10}\sqrt{461}-\frac{9}{10}\right)\right).

$$10x^{2}-5x+8=10\left(x-\left(-\frac{1}{10}\sqrt{461}-\frac{9}{10}\right)\right)\left(x-\left(\frac{1}{10}\sqrt{461}-\frac{9}{10}\right)\right)$$

To find the opposite of -\frac{1}{10}\sqrt{461}-\frac{9}{10}, find the opposite of each term.

$$10x^{2}-5x+8=10\left(x+\frac{1}{10}\sqrt{461}+\frac{9}{10}\right)\left(x-\left(\frac{1}{10}\sqrt{461}-\frac{9}{10}\right)\right)$$

To find the opposite of \frac{1}{10}\sqrt{461}-\frac{9}{10}, find the opposite of each term.

$$10x^{2}-5x+8=10\left(x+\frac{1}{10}\sqrt{461}+\frac{9}{10}\right)\left(x-\frac{1}{10}\sqrt{461}+\frac{9}{10}\right)$$

Use the distributive property to multiply 10 by x+\frac{1}{10}\sqrt{461}+\frac{9}{10}.

$$10x^{2}-5x+8=\left(10x+\sqrt{461}+9\right)\left(x-\frac{1}{10}\sqrt{461}+\frac{9}{10}\right)$$

Use the distributive property to multiply 10x+\sqrt{461}+9 by x-\frac{1}{10}\sqrt{461}+\frac{9}{10} and combine like terms.

$$10x^{2}-5x+8=10x^{2}+18x-\frac{1}{10}\left(\sqrt{461}\right)^{2}+\frac{81}{10}$$

The square of \sqrt{461} is 461.

$$10x^{2}-5x+8=10x^{2}+18x-\frac{1}{10}\times 461+\frac{81}{10}$$

Multiply -\frac{1}{10} and 461 to get -\frac{461}{10}.

$$10x^{2}-5x+8=10x^{2}+18x-\frac{461}{10}+\frac{81}{10}$$

Add -\frac{461}{10} and \frac{81}{10} to get -38.

$$10x^{2}-5x+8=10x^{2}+18x-38$$

Subtract 10x^{2} from both sides.

$$10x^{2}-5x+8-10x^{2}=18x-38$$

Combine 10x^{2} and -10x^{2} to get 0.

$$-5x+8=18x-38$$

Subtract 18x from both sides.

$$-5x+8-18x=-38$$

Combine -5x and -18x to get -23x.

$$-23x+8=-38$$

Subtract 8 from both sides.

$$-23x=-38-8$$

Subtract 8 from -38 to get -46.

$$-23x=-46$$

Divide both sides by -23.

$$x=\frac{-46}{-23}$$

Divide -46 by -23 to get 2.

$$x=2$$