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The denominator of a fraction in the simplest form is greater than the numerator by 1. If 4 is added to the numerator, and 3 is subtracted from the denominator, then the fraction itself is increased by 2 1 6 . Find the original fraction.

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thaovtp1407

Answer:

Step-by-step explanation:

Let the original fraction is: x/ x-1

And we have that:

  • 4 is added to the numerator => new numerator is: x+4
  • 3 is subtracted from the denominator => new denominator is: x -1-3 = x -4

the fraction itself is increased by 2[tex]\frac{1}{6}[/tex]

<=> [tex]\frac{x}{x-1} *2\frac{1}{6}[/tex] = [tex]\frac{x+4}{x-4}[/tex]

<=> [tex]7x^{2} -70x +24 = 0[/tex]

Solve for X then we substitue into the original fraction

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