# How do you solve #\frac { 1} { 3y - 3} + \frac { 1} { 4y - 4} = 1#?

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To solve the equation ( \frac{1}{3y - 3} + \frac{1}{4y - 4} = 1 ), follow these steps:

- Find a common denominator for the fractions on the left side of the equation.
- Combine the fractions into a single fraction.
- Solve the resulting equation for ( y ).
- Check for any extraneous solutions.

Let's proceed:

- The least common denominator (LCD) for ( 3y - 3 ) and ( 4y - 4 ) is ( (3y - 3)(4y - 4) ).
- Rewrite each fraction with the LCD: ( \frac{(4y - 4)}{(3y - 3)(4y - 4)} + \frac{(3y - 3)}{(3y - 3)(4y - 4)} = 1 )
- Combine the fractions: ( \frac{4y - 4 + 3y - 3}{(3y - 3)(4y - 4)} = 1 ) ( \frac{7y - 7}{(3y - 3)(4y - 4)} = 1 )
- Multiply both sides by the LCD to clear the fraction: ( 7y - 7 = (3y - 3)(4y - 4) )
- Expand and simplify the expression: ( 7y - 7 = 12y^2 - 24y - 12y + 12 ) ( 7y - 7 = 12y^2 - 36y + 12 ) ( 0 = 12y^2 - 43y + 19 )
- Rearrange the equation into standard quadratic form: ( 12y^2 - 43y + 19 = 0 )
- Solve the quadratic equation using factoring, the quadratic formula, or completing the square.
- Check any solutions obtained to ensure they are not extraneous.

After following these steps, you'll find the solutions for ( y ) in the given equation.

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When evaluating a one-sided 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 one-sided 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 one-sided 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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