Solve the equation for x.
-$$\frac { \mathrm { x } ^ { 2 } + 20 } { \mathrm { x } } - 1 = \frac { 4 ( \mathrm { x } + 5 ) } { \mathrm { x } }$$
A) $\{ 5 \}$
B) $\{ 3 \}$
C) $\{ 0 \}$
D) $\{ 0,5 \}$

Question

Quizplus · Accepted Answer

To solve the equation, first simplify both sides: $$\frac{x^2 + 20}{x} - 1 = \frac{4(x + 5)}{x}$$ becomes $$\frac{x^2 + 20}{x} - \frac{x}{x} = \frac{4x + 20}{x}$$ which simplifies to $$\frac{x^2 + 20 - x}{x} = \frac{4x + 20}{x}$$. This simplifies further to $$\frac{x^2 - x + 20}{x} = \frac{4x + 20}{x}$$. Since the denominators are the same, we can equate the numerators: $$x^2 - x + 20 = 4x + 20$$. Bringing all terms to one side gives $$x^2 - 5x = 0$$, which factors to $$x(x - 5) = 0$$. This gives the solutions $x = 0$ and $x = 5$. However, $x = 0$ cannot be a solution because it would make the original equation undefined (division by zero). Therefore, the only valid solution is $x = 5$.

Solve the Equation for X x2+20x−1=4(x+5)x\frac { \mathrm { x } ^ { 2 } + 20 } { \mathrm { x } } - 1 = \frac { 4 ( \mathrm { x } + 5 ) } { \mathrm { x } }xx2+20​−1=x4(x+5)​

Solve the Equation for X $\frac { \mathrm { x } ^ { 2 } + 20 } { \mathrm { x } } - 1 = \frac { 4 ( \mathrm { x } + 5 ) } { \mathrm { x } }$