Question

how can ari simplify the following expression?\\(\frac{\frac{3}{a - 3}-4}{2+\frac{1}{a - 3}}\\)\
write the numerator and\
denominator with a\
common denominator.\
then divide the numerator\
by the denominator. to do\
this, multiply the\
numerators and multiply\
the denominators.\
divide the numerator and\
the denominator by \\(a - 3\\).\
then simplify the\
numerator and simplify the\
denominator.\
divide the numerator and\
the denominator by \\(a -\
then divide the numerator\
by the denominator.\
write the numerator and\
denominator with a\
common denominator.\
then divide the numerator\
by the denominator. to do\
this, multiply the numerator\
by the reciprocal of the\
denominator.

Explanation:

To simplify a complex fraction (a fraction where numerator or denominator is a fraction), first, we need to rewrite the numerator and the denominator with a common denominator to combine the terms. For the given expression \(\frac{\frac{3}{a - 3}-4}{2+\frac{1}{a - 3}}\), the numerator has terms \(\frac{3}{a - 3}\) and \(4\) (which can be written as \(\frac{4(a - 3)}{a - 3}\)) and the denominator has terms \(2\) (which can be written as \(\frac{2(a - 3)}{a - 3}\)) and \(\frac{1}{a - 3}\). After getting a common denominator (\(a - 3\)) for both numerator and denominator, we can combine the terms. Then, to divide the numerator by the denominator, we multiply the numerator by the reciprocal of the denominator (this is the rule for dividing fractions: \(\frac{A}{B}\div\frac{C}{D}=\frac{A}{B}\times\frac{D}{C}\)). The option that describes writing numerator and denominator with a common denominator and then dividing by multiplying by the reciprocal of the denominator is the correct approach. The option with "Write the numerator and denominator with a common denominator. Then divide the numerator by the denominator. To do this, multiply the numerator by the reciprocal of the denominator." (the bottom - left option) is correct.

Answer:

The option (the bottom - left box) with text: "Write the numerator and denominator with a common denominator. Then divide the numerator by the denominator. To do this, multiply the numerator by the reciprocal of the denominator."