The process of solving Rational Equations demands identifying the variable(s) that render the equation accurate. This procedure usually requires streamlining the equation, establishing a common denominator, and resolving the ensuing polynomial equation. It's crucial to scrutinize solutions as they might be extraneous, a result of unintentionally multiplying by zero.
| Topic | Problem | Solution |
|---|---|---|
| None | $\frac{x}{(x+2)(x-2)}+\frac{4}{x-2}=\frac{3}{x+2}$ | Given the equation \(\frac{x}{(x+2)(x-2)}+\frac{4}{x-2}=\frac{3}{x+2}\) |
| None | $\frac{3}{2 x+2}+\frac{4}{x^{2}-1}=\frac{3 x}{2(x… | Given the rational equation \(\frac{3}{2 x+2}+\frac{4}{x^{2}-1}=\frac{3 x}{2(x-1)^{2}}\) |
| None | Solve each equation and check for extraneous solu… | Given the equation \(\frac{3 x+8}{x+7}=\frac{9 x}{x-4}\) |
| None | 13 The equations $\frac{24 x^{2}+25 x-47}{a x-2}=… | First, we can rewrite the equation as \(\frac{24 x^{2}+25 x-47+53}{a x-2}=-8 x-3\). |
| None | Solve $\frac{8}{x+3}+\frac{3}{x+8}=1$ | \(\frac{8}{x+3} + \frac{3}{x+8} = 1\) |
| None | $\frac{11 x^{2}}{10}-\frac{3 x}{5}=\frac{x}{2}$ | Move all terms to one side of the equation to get a quadratic equation in the form of $ax^2 + bx + … |
| None | 2. $\frac{3 x}{x-5}=\frac{2}{x+3}$ | Cross-multiply: 3x(x+3) = 2(x-5) |
| None | 1. $\frac{1}{x-2}+\frac{1}{x-2}=\frac{1}{2}$ | Combine the two fractions on the left side: \(\frac{2}{x-2} = \frac{1}{2}\) |