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:



Gemma P. GCSE Biology tutor, GCSE Chemistry tutor, GCSE Maths tutor

11 months ago

Answered by Gemma, a GCSE Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


Daniel D. GCSE Chemistry tutor, A Level Chemistry tutor, GCSE Maths t...
View profile
£20 /hr

Daniel D.

Degree: Natural Sciences Physical (Bachelors) - Cambridge University

Subjects offered: Maths, Physics+ 2 more

Further Mathematics

“About me: I am currently studying Physical Natural Sciences at Queens’ College Cambridge and next year I am going into second year. Particles, atoms and molecules are the building blocks of our world and from an understanding of thes...”

Upasana  T. GCSE Maths tutor, A Level Biology tutor
View profile
£18 /hr

Upasana T.

Degree: Medicine (Bachelors) - Birmingham University

Subjects offered: Maths, Latin+ 1 more


“About me: Hi, my name is Upasana Topiwala and I am currently in my third year of medical school at the university of Birmingham. I've taken up tutoring in order to inspire my students to appreciate the importance of science in our liv...”

MyTutor guarantee

Kyle C. A Level Computing tutor, A Level Maths tutor, GCSE Physics tu...
View profile
£18 /hr

Kyle C.

Degree: Computer Science With Electronics (Bachelors) - Edinburgh University

Subjects offered: Maths, Physics+ 1 more


“Who am I?I am a student pursuing a Computer Science degree at the University of Edinburgh. I enjoy working on theatre lighting and am also a keen fencer which is where I initially started teaching by coaching younger fencers.Sessio...”

About the author

Gemma P. GCSE Biology tutor, GCSE Chemistry tutor, GCSE Maths tutor
View profile
£20 /hr

Gemma P.

Degree: Natural Sciences (Bachelors) - Durham University

Subjects offered: Maths, Chemistry+ 1 more


“About MeI am a first year student sudying Biology and Chemistry as part of a Natural Sciences Degree at Durham University. I have always had a passion for science and teaching, both academically and non-academically, and have a broad...”

You may also like...

Posts by Gemma

Balance the Chemical Equation for the reaction of calcium carbonate with hydrochloric acid: CaCO3+ HCl -> CaCl2 + CO2 + H2O

Describe the role of blood vessels in the control of body temperature.

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

Other GCSE Maths questions

Solve the quadratic 2x^2+7x+6 by completing the square

Find x and y of these two equations: 2x - 3y = 13 and 3x + y = 3

Solve the quadratic equation x^2 + 3x + 2 = 0, by factorisation.

how do you find the original price of something that has been changed by a percentage decrease

View GCSE Maths tutors


We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss