The numerator of a fraction is 7 less than the denominator if denominator is increased by 9 and numerator by 2 we get the same fraction. What is the fractions.
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Let the denominator be x
The fraction is
x-7/x
New fraction formed =
x-7+2/x+9=x-5/x+9
x-7/x = x-5/x+9
=>(x-7)(x+9)=x(x-5)
=>x^2+9x-7x-63=x^2-5x
=>x^2+2x-63=x^2-5x
(x^2 is deduced from each side)
=>2x-63=-5x
=>2x+5x=63
=>7x = 63
=>x= 9
So,
Fraction is
x-7/x
=9-7/9
= 2/9
If it helped mark BRAINLIEST
The fraction is
x-7/x
New fraction formed =
x-7+2/x+9=x-5/x+9
x-7/x = x-5/x+9
=>(x-7)(x+9)=x(x-5)
=>x^2+9x-7x-63=x^2-5x
=>x^2+2x-63=x^2-5x
(x^2 is deduced from each side)
=>2x-63=-5x
=>2x+5x=63
=>7x = 63
=>x= 9
So,
Fraction is
x-7/x
=9-7/9
= 2/9
If it helped mark BRAINLIEST
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