How do you solve #\frac { 1} { y + 3} = \frac { 7} { y  3}  \frac { 2} { y ^ { 2}  9}#?
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To solve the equation (\frac{1}{y+3} = \frac{7}{y3}  \frac{2}{y^29}), we can follow these steps:

Start by finding a common denominator for the fractions on the right side of the equation. The common denominator in this case is ((y3)(y+3)).

Multiply both sides of the equation by the common denominator to eliminate the fractions. This gives us: ((y3)(y+3) \cdot \frac{1}{y+3} = (y3)(y+3) \cdot \left(\frac{7}{y3}  \frac{2}{y^29}\right)).

Simplify both sides of the equation. On the left side, the ((y+3)) terms cancel out, leaving us with just 1. On the right side, distribute the ((y3)(y+3)) to each term within the parentheses.

After simplifying, we are left with a quadratic equation. Rearrange the terms to bring all terms to one side of the equation, resulting in (y^2  7y  6 = 0).

Factor the quadratic equation or use the quadratic formula to find the values of (y) that satisfy the equation.

Solve for (y) by setting each factor equal to zero: (y8=0) or (y+1=0).

The solutions to the equation are (y=8) and (y=1).
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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