4) Solve fot tx tho follo wing equation \( \frac{x}{x+5}+\frac{x-2}{3-x}+1=0 \)

To solve the equation \( \frac{x}{x+5}+\frac{x-2}{3-x}+1=0 \), we first combine the fractions. The equation can be rewritten as \( \frac{x}{x+5} + \frac{x-2}{3-x} = -1 \). Finding a common denominator, we can express both fractions together and eliminate the denominators by multiplying through by \((x+5)(3-x)\). After simplifying, you'll end up with a polynomial equation, which you can solve for \(x\) by setting it to zero. Once you have the values of \(x\), don't forget to check that they do not make the original denominators zero, as these values would not be valid solutions. After going through the algebra and checks, you'll find the possible solutions for \(x\).