Questions: Solve: 35/(y+4)+5/(y+2)=6 y= If there is more than one solution, enter the solutions separated with commas. If there is no solution, enter DNE.

Solve: 35/(y+4)+5/(y+2)=6 y= If there is more than one solution, enter the solutions separated with commas. If there is no solution, enter DNE.
Transcript text: Solve: \[ \frac{35}{y+4}+\frac{5}{y+2}=6 \] $y=$ $\square$ If there is more than one solution, enter the solutions separated with commas. If there is no solution, enter DNE.
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Solution

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Solution Steps

To solve the equation \(\frac{35}{y+4}+\frac{5}{y+2}=6\), we need to find a common denominator and then solve the resulting equation for \(y\). This will involve algebraic manipulation and solving a quadratic equation.

Step 1: Set Up the Equation

We start with the equation: \[ \frac{35}{y+4} + \frac{5}{y+2} = 6 \]

Step 2: Solve for \(y\)

By manipulating the equation, we find the solutions for \(y\): \[ y = -\frac{7}{3}, \quad y = 3 \]

Final Answer

The solutions to the equation are: \[ \boxed{y = -\frac{7}{3}, 3} \]

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