# How do you solve #(x)/(2x+7)=(x-5)/(x-1)#?

Recall that you multiply to the numerator when you perform a fractional multiplication.

Thus, we have

Then

Cross multiplying is what we have just done.

We can factor this quadratic equation to get the solution we need.

These are our two responses.

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To solve the equation (x)/(2x+7)=(x-5)/(x-1), we can cross-multiply to eliminate the fractions. This gives us x(x-1) = (x-5)(2x+7). Expanding both sides of the equation, we get x^2 - x = 2x^2 - 3x - 35. Rearranging the terms, we have x^2 - 2x^2 + x - 3x + 35 = 0. Combining like terms, we obtain -x^2 - 2x + 35 = 0. To solve this quadratic equation, we can either factor it or use the quadratic formula. Factoring, we find (x-7)(x+5) = 0. Therefore, x = 7 or x = -5 are the solutions to the 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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