Rational Equations Worksheets Grade 9

1. Liam is analyzing a geometric pattern on a coordinate plane. A rectangle is drawn with vertices at A(0,0), B(10,0), C(10,5), and D(0,5). A diagonal is drawn from A to C. A smaller rectangle is formed by drawing a line from point E on AB to point F on DC, such that the line EF is parallel to AD and passes through the point where the diagonal AC intersects the vertical line x = 4. What is the length of EF?
2. (4x - 7)/(x + 9) = 3 = ?
3. Liam is designing a rectangular garden with a length that is 3 meters more than twice its width. He needs to install a decorative border along the perimeter, which requires 36 meters of border material. What are the dimensions of Liam's garden?

…and 4 more problems

1. A chemical reaction proceeds at a rate modeled by the function r(t) = (2t^2 - 8)/(t - 2) grams per minute, where t is time in minutes. Maya needs to determine the instantaneous rate of the reaction at t = 4 minutes, but the function appears undefined at t = 2. By simplifying the rational expression, what is the actual rate of the reaction at t = 4 minutes?
2. (3x + 2)/(x - 1) = 4 = ?
3. A chemical reaction follows the rate equation R(t) = (2t^2 - 8)/(t^2 - 4), where R is the reaction rate in moles per minute and t is time in minutes. At what time does the reaction rate become undefined due to a vertical asymptote?

…and 4 more problems

1. (x + 3)/(x - 2) = (2x - 1)/(x + 4)
2. Aroha is analyzing a geometric diagram on a coordinate grid. She sees a large rectangle with vertices at (0, 0), (12, 0), (12, 9), and (0, 9). Inside the rectangle, a diagonal is drawn from (0, 0) to (12, 9). A smaller rectangle is formed by the origin, a point P on the diagonal, and the lines through P parallel to the axes. If the ratio of the area of the smaller rectangle to the area of the large rectangle is 4/9, what are the coordinates of P?
3. Liam is designing a rectangular garden with an area of 48 square meters. He wants the length to be 4 meters more than the width. What are the dimensions of Liam's garden?

…and 5 more problems