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I would require to demonstrate most of this working and explaining on a white, as a keyboard can not allow a lot of the mathematical notation required to solve this, but once I have a white board I ...

To rationalise the denominator without chainging the value of the equation, multiply both the numerator and denominator by the value of the denominator.( (5+√2)/(√3) )*(√3/√3) = ( (5√3)+√6 )/3

Looking for a combination of numbers that would multiply to give (-12_ but add together to give (-1)e.g. -6, 2?....-2,6....-4,3 = yes!thus,(y-4)(y+3)

This is how the answer would be written in an exam!5x - 7 = 3x + 35x-3x = 3 + 72x = 10 x = 10/2x = 5

This is an example of implicit differentiation, where the function in question involves two variables (x and y) and it is hard to rearrange to create a neat "y=..." equation. To differentiate th...