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What is the LCD of #\frac { x + 5} { 4x - 12} - \frac { 2} { x - 3}#?

Answer 1

Genesis Allen

See solution explanation below:

Multiply the fraction on the right by #color(red)(4/4)#:

#4/4 xx 2/(x - 3) => (color(red)(4) * 2)/(color(red)(4)(x - 3)) => 8/((color(red)(4) * x) - (color(red)(4) * 3)) =>#

#8/(4x - 12)#

Therefore the LCD (Lowest Common Denominator) is: #4x - 12#

and the expression can be rewritten as:

#(x + 5)/(4x - 12) - 8/(4x - 12)#

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Answer 2

Jameson Allen

To find the LCD (Least Common Denominator) of the given expression (\frac{x+5}{4x-12} - \frac{2}{x-3}), you need to identify the common factors in the denominators and then take their least common multiple.

The denominators are (4x - 12) and (x - 3).

The prime factorization of (4x - 12) is (4(x - 3)), and the prime factorization of (x - 3) is (x - 3).

The LCD is (4(x - 3)).

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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.