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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

2 Answers

5 votes

Answer:

C


Explanation:


The equation is
x-(7)/(x)=6

LCM of the denominator on the left side gives us:


(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.

User THelloThere
by
8.8k points
3 votes

x - (7)/(x) = 6

(x^(2))/(x) - (7)/(x) = 6

(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
User Master Bee
by
8.2k points

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