what are the solutions to the equation $x - \\frac{7}{x}=6$?\n$x = - 7$ and $x = 1$\n$x=-6$ and $x =…

what are the solutions to the equation $x - \\frac{7}{x}=6$?\n$x = - 7$ and $x = 1$\n$x=-6$ and $x = - 1$\n$x=-1$ and $x = 7$\n$x = 1$ and $x = 6$

what are the solutions to the equation $x - \\frac{7}{x}=6$?\n$x = - 7$ and $x = 1$\n$x=-6$ and $x = - 1$\n$x=-1$ and $x = 7$\n$x = 1$ and $x = 6$

Answer

Explanation:

Step1: Multiply through by x

Multiply each term in $x-\frac{7}{x}=6$ by $x$ (assuming $x\neq0$) to get $x^2 - 7=6x$.

Step2: Rearrange to quadratic form

Rearrange the equation to $x^2-6x - 7 = 0$.

Step3: Factor the quadratic

Factor $x^2-6x - 7$ as $(x - 7)(x+ 1)=0$.

Step4: Solve for x

Set each factor equal to zero: $x - 7=0$ gives $x = 7$ and $x + 1=0$ gives $x=-1$.

Answer:

C. $x=-1$ and $x = 7$