Q:

** ITS TIMED HELP **How can Ari simplify the following expression? ((5)/(a-3)-4)/(2+(1)/(a-3))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.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 divide the numerator by the denominator.Divide the numerator and the denominator by a – 3. Then simplify the numerator and simplify the denominator.

Accepted Solution

A:
we have[tex]\frac{(\frac{5}{(a-3)}-4)}{(2+\frac{1}{(a-3)})}[/tex]we know that[tex]numerator=(\frac{5}{(a-3)}-4)[/tex][tex]denominator=(2+\frac{1}{(a-3)})[/tex]Step [tex]1[/tex]Write the numerator and denominator with a common denominatorNumerator[tex]\frac{5}{(a-3)}-4=\frac{5-4(a-3)}{(a-3)}=\frac{(17-4a)}{(a-3)}[/tex]Denominator[tex](2+\frac{1}{(a-3)})=\frac{2(a-3)+1}{(a-3)}=\frac{(2a-5)}{(a-3)}[/tex]Step [tex]2[/tex]Divide the numerator by the denominator[tex](\frac{(17-4a)}{(a-3)})/(\frac{(2a-5)}{(a-3)})[/tex]To do this, multiply the numerator by the reciprocal of the denominator.[tex](\frac{(17-4a)}{(a-3)})*(\frac{(a-3)}{(2a-5)})=\frac{(17-4a)}{(2a-5)}[/tex]thereforethe answer is the optionWrite 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