Verified Answer :

Panoyin

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

TaeKwonDoIsDead

Answer:

C


Step-by-step explanation:


The equation is \(x-\frac{7}{x}=6\)

LCM of the denominator on the left side gives us:

\(\frac{x^{2}-7}{x}=6\)

Cross multiplying and arranging gives us:

\(x^{2}-7=6x\\x^{2}-6x-7=0\)

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

The two numbers are: \(-7\) and \(1\).

Now we can write:

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

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

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