Final answer:
The question involves solving a quadratic equation after eliminating the common denominator. The quadratic formula is used to find the values of x, which are then checked for accuracy by substitution back into the original equation.
Step-by-step explanation:
The question asks how to solve the equation (13x)/(x+3)=(x²)/(x+3)+5. First, we observe that both sides of the equation have the common denominator (x+3). We can multiply both sides by this denominator to get rid of the fractions:
13x = x² + 5(x+3)
Next, we distribute the 5 on the right side of the equation:
13x = x² + 5x + 15
To solve for x, we set the equation to zero:
x² - 8x + 15 = 0
This is a standard quadratic equation, which we can solve using the quadratic formula. The steps include identifying a=1, b=-8, and c=15, and then substituting these values into the quadratic formula x = (-b ± √(b² - 4ac))/(2a). We can then simplify to find the values of x that satisfy the equation. Finally, we should substitute the found values of x back into the original equation to check if the solutions are valid.