Respuesta :

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

Answer:

C


Step-by-step explanation:


The equation is [tex]x-\frac{7}{x}=6[/tex]

LCM of the denominator on the left side gives us:

[tex]\frac{x^{2}-7}{x}=6[/tex]

Cross multiplying and arranging gives us:

[tex]x^{2}-7=6x\\x^{2}-6x-7=0[/tex]

This is a binomial, to factor this, we have to think of 2 numbers that multiplied gives us [tex]-7[/tex] [the constant term] and added gives us [tex]-6[/tex] [the coefficient of x].

The two numbers are: [tex]-7[/tex] and [tex]1[/tex].

Now we can write:

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

Hence, either [tex](x-7)=0[/tex] OR [tex](x+1)=0[/tex]. This gives us two solutions, [tex]x=7[/tex] and [tex]x=-1[/tex]. Answer choice C is correct.

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