What is the answer to y/(2*(y/2+1))=420 ?

The answer to y/(2*(y/2+1))=420 is y=-840/419

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y/(2*(y/2+1))=420

\frac{y}{2 \cdot ( \frac{y}{2} + 1 )} = 420

y = - \frac{840}{419}

Decimal Notation

y = - 2.00477 \dots

Solution steps

\frac{y}{2 ( \frac{y}{2} + 1 )} = 420

Simplify

\frac{y}{2 ( \frac{y}{2} + 1 )} : \frac{y}{y + 2}

\frac{y}{y + 2} = 420

Multiply both sides by

y + 2

y = 420 (y + 2)

Expand

420 (y + 2) : 420 y + 840

y = 420 y + 840

Move

420 y

to the left side

- 419 y = 840

Divide both sides by

- 419

y = - \frac{840}{419}

Verify Solutions

Find undefined (singularity) points:

y = - 2

Combine undefined points with solutions:

y = - \frac{840}{419}

\frac{( x ^{2} - 5 x + 4 )}{( x ^{2} - 4 )} = 1

a - b = \frac{a + 1}{a x}

x^{2} - 1 = \frac{1}{3 ( x + 3 )}

\frac{( x - 4.8 )}{x} = 0.18

(\frac{( x + 1 )}{( x + 2 )})^{2} = \frac{( x + 2 )}{( x + 4 )}

What is the answer to y/(2*(y/2+1))=420 ?
The answer to y/(2*(y/2+1))=420 is y=-840/419
Solve for y: y/(2*(y/2+1))=420
The solution is y=-840/419