TheBlueFox
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Please help with simplifying this rational expression.

I think I know the answer, just want to make sure my work is correct.

Please help with simplifying this rational expression I think I know the answer just want to make sure my work is correct class=

Respuesta :

joseaaronlara

Answer:

The answer to your question is y = 0

Step-by-step explanation:

                   y / (y - 5) = 5 / (y² - 25) + (y + 1) / (y + 5)

- Factor y² - 25  = (y - 5)(y + 5)

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

- Simplify

                 y / (y - 5) = [5 + (y + 1)(y - 5)] / (y - 5)(y + 5)

- Pass (y - 5)(y + 5) to the left side

                y (y + 5) = 5 + (y + 1)(y - 5)

-Expand

               y² + 5y = 5 + y² - 5y + y - 5

-Simplify

                      5y = 5 - 4y - 5

-Solve for y

                      5y + 4y = 0

                              9y = 0

                                y = 0/9

                               y = 0

Wolfyy

Heya!

Steps to solve:

[tex]\frac{y}{y-5} =\frac{y}{y^2-25} +\frac{y+1}{y+5}[/tex]

~Factor

[tex]\frac{y}{y-5} =\frac{y}{(y+5)(y-5)} +\frac{y+1}{y+5}[/tex]

~Multiply all the terms by (y + 5)(y − 5)

[tex]y(y + 5) = 5 + (y + 1)(y - 5)[/tex]

~Simplify

[tex]y^2 + 5y = y^2 - 4y[/tex]

~Subtract y² to both sides

[tex]y^2 - y^2 + 5y = y^2 - y^2 - 4y[/tex]

~Simplify

[tex]5y = -4y[/tex]

~Add 4y to both sides

[tex]5y + 4y = -4y + 4y[/tex]

~Simplify

[tex]9y = 0[/tex]

~Divide 9y to both sides

[tex]\frac{9y}{9} = \frac{0}{9}[/tex]

~Simplify

→ [tex]y = 0[/tex] ←

Best of Luck!

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