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5. The denominator of a fraction exceeds its numerator by 4. If 6 is added to the
numerator and 2 is subtracted from the denominator, the resulting fraction equals to 5.
Find the fraction.
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5. The denominator of a fraction exceeds its numerator by 4. If 6 is added to the
numerator and 2 is subtracted from the denominator, the resulting fraction equals to 5.
Find the fraction.
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Answer:
[tex]\frac{-1}{3}[/tex]
Step-by-step explanation:
Let x as n,
The denominator of a fraction exceeds its numerator by 4.
Equation 1: [tex]\frac{x}{x + 4}[/tex]
If 6 is added to the numerator and 2 is subtracted from the denominator, the resulting fraction equals to 5.
Equation 2: [tex]\frac{x + 6}{x + 4 - 2 } = 5[/tex]
[tex]\frac{x + 6}{x + 2} = 5[/tex]
Multiply both sides with ( x + 2 )
( x + 6 ) = 5( x + 2 )
( x + 6 ) = 5x + 10
Transpose and combine like terms,
-5x + x + 6 - 10 = -4x - 4
-4x/-4 = 4/-4
x = -1
Substitute to the equation 1:
[tex]\frac{-1}{( -1) + 4} = \frac{-1}{3}[/tex]
To check:
[tex]\frac{(-1) + 6}{(3) - 2} = 5/1 = 5[/tex]