鈭?x + 4 = 7 - 鈭?x How do you work out this question and express it with a rational denominator?

Assuming that x is not under square root





鈭?x + 4 = 7 - 鈭?x





鈭?x + 鈭?x = 3





x(鈭?+鈭?) = 3





x = 3/(鈭? + 鈭?)





multiply RHS with (鈭? - 鈭?)/(鈭? - 鈭?)





x = 3(鈭? - 鈭?)/(3 - 2)





x = 3(鈭? - 鈭?)鈭?x + 4 = 7 - 鈭?x How do you work out this question and express it with a rational denominator?
Get the 鈭?terms on the same side:





鈭?x + 鈭?x = 7 - 4 = 3





Square both sides


(鈭?x + 鈭?x)(鈭?x + 鈭?x) = 3(3)


3x + 2 鈭?6x^2) + 2x = 9





5x + 2x 鈭? = 9


get the square root part alone again





2x 鈭? = 9 - 5x then square both sides again


4x^2 (6) = (9-5x)(9-5x)


24x^2 = 81 - 90x + 25x^2





Make it = 0


0 = x^2 - 90x + 81





then solve


check the math , these are really big numbers鈭?x + 4 = 7 - 鈭?x How do you work out this question and express it with a rational denominator?
(鈭? + 鈭?)x = 3





x = 3/(鈭? + 鈭?)





Multiply top and bottom by (鈭? - 鈭?)





= 3(鈭? - 鈭?)
鈭?x + 鈭?x = 3


x(鈭? + 鈭?) = 3


x = 3 / (鈭?+鈭?)


x = 3(鈭?-鈭?)/(鈭?+鈭?)(鈭?-鈭?)





multiply above and below by (鈭?-鈭?)


the denominator becomes 1 because it is the factorisation for the difference of squares, giving 3-2 = 1





x = 3(鈭?-鈭?) = 3鈭? - 3鈭?
First step, bring the 鈭?x to the left side and the 4 to the right side, like this:


鈭?x + 鈭?x = 7 - 4


then, collect like terms:


(鈭? + 鈭?)x = 3


Isolate x, we have:


x = 3/(鈭? + 鈭?)





Now, to rationalize the fraction, we multiply the denominator of this fraction by its conjugate, namely: (鈭? - 鈭?) i.e. just change the sign [of course you have to multiply the numerator by (鈭? - 鈭?) as well so that you are multiplying the original fraction by 1 so to not change the value)





then, we have x =


3/(鈭? + 鈭?) * (鈭? - 鈭?)/(鈭? - 鈭?)


= (3鈭? - 3鈭?)/1


and that is the final answer





hope that helps