How do you solve #8/(x-4) -3=1/(x-10)#?
This means that any possible solution set will not include thes values. In other words, you need
This will get you
This is of course equivalent to
Use the quadratic formula to find the two roots of this quadratic equation
Therefore, you have
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To solve the equation ( \frac{8}{x-4} - 3 = \frac{1}{x-10} ), follow these steps:
- Find a common denominator for the fractions, which is ( (x-4)(x-10) ).
- Rewrite the equation with the common denominator: ( \frac{8(x-10)}{(x-4)(x-10)} - \frac{3(x-4)}{(x-4)(x-10)} = \frac{1}{x-10} ).
- Combine the fractions: ( \frac{8(x-10) - 3(x-4)}{(x-4)(x-10)} = \frac{1}{x-10} ).
- Distribute and simplify: ( \frac{8x - 80 - 3x + 12}{(x-4)(x-10)} = \frac{1}{x-10} ).
- Combine like terms: ( \frac{5x - 68}{(x-4)(x-10)} = \frac{1}{x-10} ).
- Cross multiply: ( (5x - 68)(x-10) = (x-4) ).
- Expand and simplify: ( 5x^2 - 50x - 68x + 680 = x - 4 ).
- Rearrange terms: ( 5x^2 - 118x + 684 = 0 ).
- Factor the quadratic equation, if possible, or use the quadratic formula to find the solutions for (x).
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To solve the equation ( \frac{8}{x-4} - 3 = \frac{1}{x-10} ):
- First, simplify the equation by finding a common denominator for the fractions.
- Then, combine like terms.
- Next, solve for ( x ).
- Finally, check for extraneous solutions.
The process involves cross-multiplication, simplification, and solving the resulting quadratic 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.
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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