A rational value is any number that can by formed by taking the quotient of two integers. This basically tells us that it does not have a fractional portion to it. Solving rational inequalities is very much like solving equations, which we should have a good handle on by this point. You start by simplifying the inequality that you are given. The next step is to evaluate it at a point of interest, the x-axis (noted as x = 0) is always nice. The last thing to do is run test points to see where it lies.
We can solve rational inequalities as we resolve the polynomial inequalities. But you will find denominators in rational figures. Therefore, it may have some areas where you can't define them. You have to be a little bit careful while solving the problems. You will find zeroes under the numerator and undefined points under denominator while solving rational inequality. You can divide the number lines into intervals by using zeroes and uncleared points. As a result, you will find the sign of the rational on each range. Solve: x2 + 3x + 2/x2 - 16 ≥ 0 Factorize the following;x2 + 3x + 2/x2- 16 = (x + 2)(x+1)/(x+4)(x-4) When you find zero nominators of polynomial fraction, you will keep the nominator equal to zero and the solution like the following one; (x+2)(x+1) = 0, x+2 = 0 or x + 1 = 0, x = -2 or x = -1 You will apply the same rule in the following solution; (x+4)(x-4) = 0, x+4 = 0 or x + 4 = 0, x = -4 or x = -4 Divide the number line into five intervals by the above answers that are -4, -2, -1, and 4. (-infinity - 4), (-4,-2), (-2,-1),(-1,4), and (4, +infinity). These worksheets explain how to solve and graphically express (on number lines) equations containing inequalities. The lesson specifically show students how to place these values on a number line.