# How do you multiply #(f^2 - 7f + 10)/( f^3 - 7f^2 + 7f - 49) *( f^2 - 49)/( 2f^3-10*f^2) #?

Factoring functions like this can be a bit hard, specially for non-quadratics, but I've found that this is a good source..

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To multiply the given expressions, we can first factorize the numerator and denominator of each fraction.

The numerator of the first fraction, (f^2 - 7f + 10), can be factored as (f - 5)(f - 2). The denominator of the first fraction, (f^3 - 7f^2 + 7f - 49), cannot be factored further.

The numerator of the second fraction, (f^2 - 49), can be factored as (f - 7)(f + 7). The denominator of the second fraction, (2f^3 - 10*f^2), can be factored as 2f^2(f - 5).

Now, we can cancel out common factors between the numerators and denominators.

Canceling out (f - 5) from the first fraction's numerator and denominator, we are left with (f - 2)/(f^3 - 7f^2 + 7f - 49).

Canceling out (f - 7) from the second fraction's numerator and denominator, we are left with (f + 7)/(2f^2(f - 5)).

Multiplying these simplified fractions together, we get (f - 2)(f + 7)/(f^3 - 7f^2 + 7f - 49)(2f^2(f - 5)).

This is the final result of multiplying the given expressions.

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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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