notjoro
27

# What are the solutions to the equation x-7/x=6? a. x=-7 and x=1 b. x=-6 and x=-1 c. x=-1 and x=7 d. x=1 and x=6

$x - \frac{7}{x} = 6$ $\frac{x^{2}}{x} - \frac{7}{x} = 6$ $\frac{x^{2} - 7}{x} = 6$ $x^{2} - 7 = 6x$ $x^{2} - 6x - 7 = 0$ $x^{2} - 7x + x - 7 = 0$ $x(x) - x(7) + 1(x) - 1(7) = 0$ $x(x - 7) + 1(x - 7) = 0$ $(x + 1)(x - 7) = 0$ $x + 1 = 0$    $or$    $x - 7 = 0$ $x = -1$    $or$    $x = 7$