the numerator of a fraction is less than the denominator. if 1 added to the denominator it becomes 1/2 find the fraction
Answers
Answer:
Let the numerator be x
Therefore, denominator is x+2
The fraction is
x+2
x
Now,
x+2
x
+
x+3
x+1
=
15
19
=>
(x+2)(x+3)
x
2
+3x+(x+1)(x+2)
=
15
19
=>
(x+2)(x+3)
x
2
+3x+x
2
+3x+2
=
15
19
=>15(x
2
+3x+x
2
+3x+2)=19(x+2)(x+3)
=>15(2x
2
+6x+2)=19(x
2
+5x+6)
=>30x
2
+90x+30=19x
2
+95x+114
=>11x
2
−5x−84=0
=>11x
2
−33x+28x−84=0
=>11x(x−3)+28(x−3)=0
=>(11x+28)(x−3)=0
Therefore, x=3 or x=−
11
28
For x=−
11
28
, denominator is :-
−
11
28
+2=
11
−28+22
=−
11
6
So, the fraction is
−
11
6
−
11
28
=
6
28
=
3
14
Now adding 1 on both numerator and denominator we get
4
15
But,
3
14
+
4
15
=
15
19
∴x=3 and denominator is x+2=3+2=5
∴ the fraction is
5
3
Let the numerator be x
Therefore, denominator is x+2
The fraction is
x+2
x
Now,
x+2
x
+
x+3
x+1
=
15
19
=>
(x+2)(x+3)
x
2
+3x+(x+1)(x+2)
=
15
19
=>
(x+2)(x+3)
x
2
+3x+x
2
+3x+2
=
15
19
=>15(x
2
+3x+x
2
+3x+2)=19(x+2)(x+3)
=>15(2x
2
+6x+2)=19(x
2
+5x+6)
=>30x
2
+90x+30=19x
2
+95x+114
=>11x
2
−5x−84=0
=>11x
2
−33x+28x−84=0
=>11x(x−3)+28(x−3)=0
=>(11x+28)(x−3)=0
Therefore, x=3 or x=−
11
28
For x=−
11
28
, denominator is :-
−
11
28
+2=
11
−28+22
=−
11
6
So, the fraction is
−
11
6
−
11
28
=
6
28
=
3
14
Now adding 1 on both numerator and denominator we get
4
15
But,
3
14
+
4
15
=
15
19
∴x=3 and denominator is x+2=3+2=5
∴ the fraction is
5
3
Let the numerator be x
Therefore, denominator is x+2
The fraction is
x+2
x
Now,
x+2
x
+
x+3
x+1
=
15
19
=>
(x+2)(x+3)
x
2
+3x+(x+1)(x+2)
=
15
19
=>
(x+2)(x+3)
x
2
+3x+x
2
+3x+2
=
15
19
=>15(x
2
+3x+x
2
+3x+2)=19(x+2)(x+3)
=>15(2x
2
+6x+2)=19(x
2
+5x+6)
=>30x
2
+90x+30=19x
2
+95x+114
=>11x
2
−5x−84=0
=>11x
2
−33x+28x−84=0
=>11x(x−3)+28(x−3)=0
=>(11x+28)(x−3)=0
Therefore, x=3 or x=−
11
28
For x=−
11
28
, denominator is :-
−
11
28
+2=
11
−28+22
=−
11
6
So, the fraction is
−
11
6
−
11
28
=
6
28
=
3
14
Now adding 1 on both numerator and denominator we get
4
15
But,
3
14
+
4
15
=
15
19
∴x=3 and denominator is x+2=3+2=5
∴ the fraction is
5
3
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