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How do you simplify #(2x^2-8)/(4x-8)#?

Answer 1

Eva Abramson

#(2x^2-8)/(4x-8)# = # (2(x^2-4))/(4(x-2))#

# = (2(x^2-2^2))/(4(x-2))#

We know that #color(blue)(a^2 - b^2 = (a+b)(a-b)#

# =(2(x+2)cancel((x-2))) / (4cancel((x-2))#

# = (2(x+2))/4#

# =color(green)((x+2)/2#

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Answer 2

Genesis Allen

To simplify (2x^2-8)/(4x-8), we can factor out a common factor of 2 from both the numerator and the denominator. This gives us (2(x^2-4))/(4(x-2)). Next, we can simplify further by canceling out the common factor of 2 in the numerator and the denominator. This leaves us with (x^2-4)/(2(x-2)). Finally, we can factor the numerator as a difference of squares, giving us ((x+2)(x-2))/(2(x-2)). The (x-2) terms cancel out, resulting in the simplified expression of (x+2)/2.

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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.