Rational Equations Worksheets Grade 9

1. A chemical reaction follows a rate modeled by the rational function R(t) = (3t^2 - 12) / (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?
2. Tane is analyzing a geometric pattern on a coordinate grid. A right triangle is drawn with vertices at A(0,0), B(14,0), and C(0,9). Inside this triangle, a rectangle is inscribed such that one side lies along the x-axis from (0,0) to (8,0), and the opposite side touches the hypotenuse of the triangle at points where the rectangle's top-left corner is at (0,5) and top-right corner is at (8,5). What is the area of the rectangular region inside the triangle?
3. A chemical reaction follows a rate model where the reaction rate R is given by R(x) = (2x^2 - 5x + 3)/(x - 1), where x represents the concentration of a reactant in moles per liter. At what concentration does the reaction rate reach 7 moles per liter per minute?

…and 3 more problems

1. (4x - 7)/(x + 9) = 3 = ?
2. A rectangular garden has a length that is 3 meters more than its width. The area of the garden is 70 square meters. If the width is represented by w meters, which equation can be used to find the width? Solve the equation to find the width of the garden.
3. (3x + 2)/(x - 1) = 4 = ?

…and 6 more problems

1. Mere is planning a road trip. The distance to the destination is 455 kilometers. If Mere drives at a constant speed, the time taken, in hours, is given by the equation 455/v = 5, where v is the speed in kilometers per hour. What is Mere's driving speed?
2. A chemical reaction produces a compound at a rate modeled by the function R(t) = (3t^2 - 12)/(t - 2), where t is time in minutes and R(t) is the production rate in grams per minute. Maya needs to determine the instantaneous production rate at t = 2 minutes, but the function appears undefined at this point. What is the actual production rate at t = 2 minutes?
3. On a coordinate plane, a rectangle has vertices at A(0,0), B(12,0), C(12,8), and D(0,8). A diagonal is drawn from A to C. A point P lies on diagonal AC such that the ratio of the length of AP to the length of PC is 3:5. What is the x-coordinate of point P?

…and 4 more problems