Question

The denominator of a fraction is one more than twice the numerator. If both numerator and denominator are decreased by seven, the simplified result is -12. Find the original fraction. (Do not simplify.)

Answer 1

To solve this problem, use algebraic equations to represent the numerator and denominator of the fraction. By setting up and simplifying the equation, we find that the original fraction is -12/25.

Step-by-step explanation:

To solve this problem, we can use algebraic equations. Let's assign variables to the numerator and denominator of the fraction. Let x be the numerator and 2x+1 be the denominator. We can set up the equation x/(2x+1) = -12. To solve for x, we multiply both sides of the equation by (2x+1) to get x = -12(2x+1).

Next, we simplify the equation by distributing -12 on the right side, which gives us x = -24x - 12. We can then combine like terms by adding 24x to both sides of the equation, resulting in 25x = -12. Finally, we divide both sides by 25 to solve for x, giving us x = -12/25.

The original fraction is x/(2x+1), so substituting x = -12/25 into the expression, we get (-12/25)/(2(-12/25)+1). This simplifies to -12/25.