Mathematics
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

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(1) Answers
Carry751

[latex]x - \frac{7}{x} = 6[/latex] [latex]\frac{x^{2}}{x} - \frac{7}{x} = 6[/latex] [latex]\frac{x^{2} - 7}{x} = 6[/latex] [latex]x^{2} - 7 = 6x[/latex] [latex]x^{2} - 6x - 7 = 0[/latex] [latex]x^{2} - 7x + x - 7 = 0[/latex] [latex]x(x) - x(7) + 1(x) - 1(7) = 0[/latex] [latex]x(x - 7) + 1(x - 7) = 0[/latex] [latex](x + 1)(x - 7) = 0[/latex] [latex]x + 1 = 0[/latex]    [latex]or[/latex]    [latex]x - 7 = 0[/latex] [latex]x = -1[/latex]    [latex]or[/latex]    [latex]x = 7[/latex]

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