What is the answer to (1-2y)/(3-y)+y= 1/(y+2) ?

The answer to (1-2y)/(3-y)+y= 1/(y+2) is y\approx 0.27389…,y\approx 1.37720…,y\approx-2.65109…

Solve for y: (1-2y)/(3-y)+y= 1/(y+2)

The solution is y\approx 0.27389…,y\approx 1.37720…,y\approx-2.65109…

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\frac{1 - 2 y}{3 - y} + y = \frac{1}{y + 2}

y \approx 0.27389 \dots, y \approx 1.37720 \dots, y \approx - 2.65109 \dots

Solution steps

\frac{1 - 2 y}{3 - y} + y = \frac{1}{y + 2}

Multiply by LCM

(1 - 2 y) (y + 2) + y (- y + 3) (y + 2) = - y + 3

Solve

(1 - 2 y) (y + 2) + y (- y + 3) (y + 2) = - y + 3 : y \approx 0.27389 \dots, y \approx 1.37720 \dots, y \approx - 2.65109 \dots

y \approx 0.27389 \dots, y \approx 1.37720 \dots, y \approx - 2.65109 \dots

Verify Solutions

Find undefined (singularity) points:

y = 3, y = - 2

Combine undefined points with solutions:

y \approx 0.27389 \dots, y \approx 1.37720 \dots, y \approx - 2.65109 \dots

\frac{m}{m + 9} = \frac{63}{22}

\frac{6}{a + 1} = \frac{a}{a - 1}

60 w - \frac{270}{w ^{2}} = 0

\frac{22}{n} = \frac{88}{100}

0 = 1 - \frac{1}{x}

What is the answer to (1-2y)/(3-y)+y= 1/(y+2) ?
The answer to (1-2y)/(3-y)+y= 1/(y+2) is y\approx 0.27389…,y\approx 1.37720…,y\approx-2.65109…
Solve for y: (1-2y)/(3-y)+y= 1/(y+2)
The solution is y\approx 0.27389…,y\approx 1.37720…,y\approx-2.65109…