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How do you multiply #(x-3)/(x-5)=3/(x-5)#?

Answer 1

Genesis Allen

We first determine that #x!=5#, as this would make the denominators #=0#, which is not allowed.

Then we can cancel out the #(x-5)# on both sides (=multiply both sides by #x-5#):

#->(x-3)=3->x=6#

Answer : #x=6#

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Answer 2

Jace Anderson

To solve the equation (x-3)/(x-5) = 3/(x-5), we can start by cross-multiplying. This means multiplying the numerator of the first fraction with the denominator of the second fraction, and vice versa.

(x-3) * (x-5) = 3 * 1

Expanding the left side of the equation:

x^2 - 5x - 3x + 15 = 3

Combining like terms:

x^2 - 8x + 15 = 3

Moving the constant term to the right side:

x^2 - 8x + 15 - 3 = 0

Simplifying:

x^2 - 8x + 12 = 0

Now, we can factor the quadratic equation:

(x - 2)(x - 6) = 0

Setting each factor equal to zero:

x - 2 = 0 or x - 6 = 0

Solving for x:

x = 2 or x = 6

Therefore, the solutions to the equation (x-3)/(x-5) = 3/(x-5) are x = 2 and x = 6.

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Answer from HIX Tutor

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.