1/x+ 8/5x=1? How do i solve for x

also, how to solve:

6/x(x-6) - 1/x-6 = 0?

This is another way to do it.

1/x+8/5x=1

Make the fractions have like denominators.

5/5x+8/5x=1

Simplify

13/5x=1

Multiply both sides by 5x

13=5x

Divide by 5.

13/5=x

5x2 means 5 multiplied with square of x



1/x+8/5x equals 1
on dividing

5x+8x/5x2 equals 1

send 5x2 to right hand side
i.e.
5x+8x equals 5x2
now add 5x and 8x which is 13x
now
13x equals 5x2
cancels one x of 5x2 with x of 13x

you get
13 equals to 5x
or 7 equals 13/5


answer to your next question

6/x(x-6)-1/x-6 equals zero

since it is zero at right hand side shift the term -1/x-6 to right hand side it will become positive
so now equation would be

6/x(x-6) equals 1/x-6

now you can cancel x-6 on both sides
so
equation would be
6/x equals 1
shift x to right hand side
you will get x equals 6

i tried my best to make u undertand this
i hope you will understand

Isolate x