x + 1 / x = 17 / 4 , Solve for ' x ' algebrcally ?

multiply both sides by x.
x^2 + 1 = 17x/4
x^2 - 17x/4 + 1 = 0
multiply both sides by 4.
4x^2 - 17x + 4 =0, now it became a quadratic equation.
use quadratic formula
x = [-b +/-sqrt(b^2 - 4ac)] / (2a) and find the value for x.

x + 1 / x = 17 / 4

=> 4x^2 - 17x +4 = 0

=> 4x^2 - 16x - x + 4 =0

=> 4x ( x - 4) - ( x - 4 ) = 0

=> ( 4x - 1) ( x - 4 ) = 0

=> ( 4x - 1) = 0 or ( x - 4 ) = 0

=> x = 1/4 or x = 4

x+1/x=17/4
(x^2+1)/x=17/4
from the denominator x=4
substitute in the numinator x^2+1=17 => x=4 true

4(x^2+1)=17x

4x^2-17x+4=0
(x-4)(4x-1)
x=1/4 or x=4

There's an ambiguity in your question; do you mean x + (1 / x) = 17/4 or (x + 1)/ x = 17/4?

yeah i had a lot hassle doing those style of issues too! yet now i comprehend. besides, right this is how: 2(x - 7) = 4(3x + a million) use distributive belongings 2x - 7 = 12x + a million use subtraction belongings of equality to subtract 2x on the two facets 2x-2x-7 = 12x-2x +a million ?consequences? 7 = 10x + a million use subtraction belongings of equality to subtract a million on the two facets 7-a million = 10x +a million-a million ?consequences? 6 = 10x use branch belongings of equality to divide 10 on the two facets 6/10 = 10x/10 ?consequences? 0.6 = x desire this helps! ^-^

x+1 = 17
-----------------------------
x 4

4(x+1)=17x
4x+4=17x
4=13x
13/4=x

(x + 1)/x = 17/4
x + 1 = x(17/4)
x + 1 = 17x/4
4(x + 1) = 17x
4x + 4 = 17x
4x - 17x = -4
-13x = -4
x = 4/13