how can ari simplify the following expression?\n\\(\\frac{\\frac{5}{a - 3}-4}{2+\\frac{1}{a - 3}}\\)\nwrite…
how can ari simplify the following expression?\n\\(\\frac{\\frac{5}{a - 3}-4}{2+\\frac{1}{a - 3}}\\)\nwrite 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.\nwrite 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.\ndivide the numerator and the denominator by a - 3. then divide the numerator by the denominator.\ndivide the numerator and the denominator by a - 3. then simplify the numerator and simplify the denominator.
Answer
Explanation:
Step1: Combine terms in numerator and denominator
The numerator $\frac{5}{a - 3}-4=\frac{5-4(a - 3)}{a - 3}=\frac{5-4a + 12}{a - 3}=\frac{-4a+17}{a - 3}$. The denominator $2+\frac{1}{a - 3}=\frac{2(a - 3)+1}{a - 3}=\frac{2a-6 + 1}{a - 3}=\frac{2a-5}{a - 3}$. So the original expression becomes $\frac{\frac{-4a + 17}{a - 3}}{\frac{2a-5}{a - 3}}$.
Step2: Divide by multiplying by reciprocal
To divide by a fraction, we multiply the numerator by the reciprocal of the denominator. So $\frac{\frac{-4a + 17}{a - 3}}{\frac{2a-5}{a - 3}}=\frac{-4a + 17}{a - 3}\times\frac{a - 3}{2a-5}=\frac{-4a + 17}{2a-5}$. This is achieved by first writing the numerator and denominator with a common denominator and then multiplying the numerator by the reciprocal of the denominator.
Answer:
The correct option is: 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.