Question

If x+1/x=7, find:x-1/x

Answer 1

-5

Explanation:

First, let us find the value of x.

`\sf (x+1)/(x)=7\\\\ Multiply\:both\:sides\:by\:x\\\\x+1=7x\\\\Subtract \:x\:from\:both\:sides.\\\\1=6x\\\\Divide\:both\:sides\:by\:6.\\\\(1)/(6)=x`

And now let us find the value of the given expression by replacing x with 1/6.

`\sf (x-1)/(x) \\\\\\((1)/(6)-1 )/((1)/(6) ) \\\\\\Make\: the \:denominator \:the\: same\: to \:do \:the\:subtraction\:of\:the\:fractions.\\\\\\((1)/(6)-(1*6)/(1*6) )/((1)/(6) )\\\\\\((1)/(6)-(6)/(6) )/((1)/(6) ) \\\\\\(-(5)/(6) )/((1)/(6) ) \\\\\\-(5)/(6) / (1)/(6) \\\\\\`

`\sf To\:divide,\\ \: the\: fractions\: reverse \:the \:numerator \:and \:denominator\: of\: the\: second\: fraction,\\\:and\:multiply \:the\:fractions.\\\\-(5)/(6) *(6)/(1)\\\\ -5`

Answer 2

-5

Explanation:

x+1/x=7

Solve for x.

Multiply by x

x(x+1/x)=7x

x+1 = 7x

Subtract x from each side

x+1-x = 7x-x

1 = 6x

Divide by 6

1/6 = 6x/6

1/6 =x

Now we can find (x-1)/x

1/6 -1

--------------

1/6

Subtract

-5/6

-------

1/6

Multiply top and bottom by 6

-5