Simplify (x^2-9)/2x^2+5x-3

To simplify this equation we need factorize both quadratic equations into brackets, so we can then cancel out terms on both the denominator and numerator.

For the first euqation: x2-9, there is no x value so when we split the quadratic equation into 2 brackets we know our values must add up to 0. As it is x2 we know that each bracket has an x.

(x   )(x   ), becuase there is a minus sign we can deduce that one of the brackets must have a negative sign. Therefore as 9 is a square number we can deduce that it is (x-3)(x+3).

For the second quadratic there is a 2x2 so we know that there must be a 2x and an x in each bracket, (2x   )(x   ). We must then think of 2 values that times together to make -3. We know that one of our values must be neative and one positive in order to make -3. (2 negatives or 2 positives would both make a positive). Values we may have are: -1,3 or 1,-3.

Therefore by methods of trial and error our second qudratic is: (2x-1)(x+3)

We can then put both factorised quadratics back into the original equation and cancel out an brackets that are the same:



We can see that (x+3) is common on both the numerator and denominator so it can be cancelled out. Therfore our simplified equation is:



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