Exercise
$\frac{x}{x-8}+\frac{6}{x+2}=\frac{x^2}{x^2-10x+16}$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the rational equation x/(x-8)+6/(x+2)=(x^2)/(x^2-10x+16). Factor the trinomial x^2-10x+16 finding two numbers that multiply to form 16 and added form -10. Rewrite the polynomial as the product of two binomials consisting of the sum of the variable and the found values. Multiply both sides of the equation by \left(x-2\right)\left(x-8\right). The least common multiple (LCM) of a sum of algebraic fractions consists of the product of the common factors with the greatest exponent, and the uncommon factors.
Solve the rational equation x/(x-8)+6/(x+2)=(x^2)/(x^2-10x+16)
Final answer to the exercise
$x=\frac{64+\sqrt{2560}}{8},\:x=\frac{64-\sqrt{2560}}{8}$