Solve y=1/x+2/x-3/4x-3+2;quadx=1/2

$$y = \frac { \frac { 1 } { x } + \frac { 2 } { x - 3 } } { 4 x - 3 } + 2 ; \quad x = \frac { 1 } { 2 }$$

Solve for y, x

$$x=\frac{1}{2}=0.5$$

$$y=\frac{4}{5}=0.8$$

Solution Steps

Consider the first equation. Insert the known values of variables into the equation.

$$y=\frac{\frac{1}{\frac{1}{2}}+\frac{2}{\frac{1}{2}-3}}{4\times \frac{1}{2}-3}+2$$

Divide 1 by \frac{1}{2} by multiplying 1 by the reciprocal of \frac{1}{2}.

$$y=\frac{1\times 2+\frac{2}{\frac{1}{2}-3}}{4\times \frac{1}{2}-3}+2$$

Multiply 1 and 2 to get 2.

$$y=\frac{2+\frac{2}{\frac{1}{2}-3}}{4\times \frac{1}{2}-3}+2$$

Subtract 3 from \frac{1}{2} to get -\frac{5}{2}.

$$y=\frac{2+\frac{2}{-\frac{5}{2}}}{4\times \frac{1}{2}-3}+2$$

Divide 2 by -\frac{5}{2} by multiplying 2 by the reciprocal of -\frac{5}{2}.

$$y=\frac{2+2\left(-\frac{2}{5}\right)}{4\times \frac{1}{2}-3}+2$$

Multiply 2 and -\frac{2}{5} to get -\frac{4}{5}.

$$y=\frac{2-\frac{4}{5}}{4\times \frac{1}{2}-3}+2$$

Subtract \frac{4}{5} from 2 to get \frac{6}{5}.

$$y=\frac{\frac{6}{5}}{4\times \frac{1}{2}-3}+2$$

Multiply 4 and \frac{1}{2} to get 2.

$$y=\frac{\frac{6}{5}}{2-3}+2$$

Subtract 3 from 2 to get -1.

$$y=\frac{\frac{6}{5}}{-1}+2$$

Express \frac{\frac{6}{5}}{-1} as a single fraction.

$$y=\frac{6}{5\left(-1\right)}+2$$

Multiply 5 and -1 to get -5.

$$y=\frac{6}{-5}+2$$

Fraction \frac{6}{-5} can be rewritten as -\frac{6}{5} by extracting the negative sign.

$$y=-\frac{6}{5}+2$$

Add -\frac{6}{5} and 2 to get \frac{4}{5}.

$$y=\frac{4}{5}$$

The system is now solved.

$$y=\frac{4}{5} x=\frac{1}{2}$$