Solving Rational Equations

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.

The problems about Solving Rational Equations

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: $\frac{2}{x - 2} = \frac{1}{2}$