the denominator of a rational number is greater than it 's numerator by 8. if the numerator is increased by 17and the denominator is decreased by 1 , the obtained is
3/2.
find the RATIONAL NUMBER
Answers
Answer:) The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is \frac{3}{2}
2
3
. Find a rational number.
Step-by-step explanation:Let the numerator of a rational number be x then the denominator is x+8.
Therefore, Rational number = \frac{x}{x+8}
x+8
x
According to the question,
\frac{x+17}{x+8-1}=\frac{3}{2}
x+8−1
x+17
=
2
3
\Rightarrow\ \frac{x+17}{x+7}=\frac{3}{2}⇒
x+7
x+17
=
2
3
\Rightarrow\ 2\left(x+17\right)=3\left(x+7\right)⇒ 2(x+17)=3(x+7)
\Rightarrow\ 2x+34=3x+21⇒ 2x+34=3x+21
\Rightarrow\ 2x-3x=21-34⇒ 2x−3x=21−34
\Rightarrow\ -x=-13⇒ −x=−13
\Rightarrow\ x=13⇒ x=13
Hence, the required rational number
=\ \frac{x}{x+8}=\frac{13}{13+8}=\frac{13}{21}=
x+8
x
=
13+8
13
=
21
13