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The easiest way to solve this is to split the fraction into partials.Using partial fractions, we get A/(x-3)+B/x=x+3/(x(x-3)) implies Ax+B(x-3)=x+3We want to find the values of A and B that solve this, so...

We want to start with “the square of an odd number” and show something. Remember that any odd number can be expressed as 2n+1 (an even number is 2n, and any odd number is 1 larger than an...

First, label the equations 1 and 2:1: 7x+y=1 and 2: 2x^2-y=3Rearrange equation 2 in terms of yy=2x^2-3Now substitue the rearranged version of equation 2 into 1 to give7x+2x^2-3=1.Bring all the values to t...

The stationary points are located where the gradient of the function is equal to 0. The first derivative of the function describes the gradient so we must differentiate the function to find dy/dx.
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Only factors of 2 are 1 and 2, therefore solution will take form of (2x + a)(x + b) to get 2x² term. Only factors of 3 are 1 and 3 therefore a and b are either 1 or 3. Playing around and intuit...