How can ari simplify the following expression?

Asked by maham237 @ 16/12/2020 in Mathematics viewed by 1058 People

((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.

Answered by maham237 @ 16/12/2020

we have

$\frac{(\frac{5}{(a-3)}-4)}{(2+\frac{1}{(a-3)})}$

we know that

$numerator=(\frac{5}{(a-3)}-4)$

$denominator=(2+\frac{1}{(a-3)})$

Step $1$

Write the numerator and denominator with a common denominator

Numerator

$\frac{5}{(a-3)}-4=\frac{5-4(a-3)}{(a-3)}=\frac{(17-4a)}{(a-3)}$

Denominator

$(2+\frac{1}{(a-3)})=\frac{2(a-3)+1}{(a-3)}=\frac{(2a-5)}{(a-3)}$

Step $2$

Divide the numerator by the denominator

$(\frac{(17-4a)}{(a-3)})/(\frac{(2a-5)}{(a-3)})$

To do this, multiply the numerator by the reciprocal of the denominator.

$(\frac{(17-4a)}{(a-3)})*(\frac{(a-3)}{(2a-5)})=\frac{(17-4a)}{(2a-5)}$

therefore

the answer is the option

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

How can ari simplify the following expression?

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