To solve this equation, we need to collect all of the x^2 terms and the x terms together. To do this we should start by getting rid of the fraction on the left-hand side by multiplying both sides by the denominator (x+1). This gives 4-2x = x(x+1). We then need to get rid of the bracket by expanding it, leaving us with 4-2x = x^2 + x. We then need to collect like terms together. After this is done we can rearrange the equation into the quadratic equation x^2 + 3x - 4 = 0.

Next we need to solve this equation to find all of the possible values of x. Two ways of doing this are either by using the quadratic formula or factorising it into two brackets multiplied together. If we choose to facotrise, we get (x+4)(x-1) which expands to give x^2 + 3x - 4. As the equation is equal to 0, the two possible values of x which make the equation true are x=1 and x=-4.

Solve the following equation 2x^2+6x=8

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