2y/y(5y-1) + 5/5y-1

Question

2y/y(5y-1) + 5/5y-1

compassionate · Answer

$$\frac{ 2y }{ y(5y - 1)} + \frac{ 5 }{ 5y - 1 }$$

Is this your equation, hun?

anonymous · Answer

Yes sure is

compassionate · Answer

Distribute the y in the denominator of the first fraction.

anonymous · Answer

5y^2-1y

anonymous · Answer

Im not sure what you were meaning there is that right

tkhunny · Answer

The denominator is already factored for you.  Why not exploit that to enforce the common denominator?

$\dfrac{2y}{y(5y-1)}+\dfrac{5}{5y-1}\cdot\dfrac{y}{y} = \dfrac{7y}{y(5y-1)}$

anonymous · Answer

oh ok I see what you were saying thank you for the help that was a lot easier than I thought.

compassionate · Answer

Good explanation, tkhunny.

tkhunny · Answer

Well, that may be overkill in this case.  There is still simplification to do.  We might have done it up front.

$\dfrac{2y}{y(5y-1)} + \dfrac{5}{5y-1} = \dfrac{y}{y}\dfrac{2}{5y-1} + \dfrac{5}{5y-1} = \dfrac{2}{5y-1} + \dfrac{5}{5y-1} = \dfrac{7}{5y-1}$, as long as $y \ne 0$