Is extension maths for HSC compulsory for doing engineering at uni?

I Have just started an engineering course at uni, please help with these maths questions!!!? 10points?

• Hi, I have been doing a engineering course at uni lately and I am having a lot of troubles with these very hard maths questions. Could someone please hep me get the correct answers to these questions and also show me the working out so i can understand how you got the answer. This would be very very appreciated if someone could help me! I cant type them on here exactly the same so ill just write a / when there is a fraction. So here they are : SIMPLIFY: 1. (2x-1)(x² + 5x - 6) / (4x² - 1)(x - 1) 2. x - 3 / x ÷ x² - 9 / 2x 3.√3 - √9 - √27 + √81 4. (3+ √3)(1 - 1/ √3) RATIONALIZE : 5. 1/ √2 - 1 6. 5/ 2√3 7. 11/ 2√3 - 1 8. 1 - √3/3 / 1+√3/3 9. SHOW THAT : 2 √3 + 1 / 2 √3 - 1 + 2 √3 - 1 / 2 √3 + 1 IS A RATIONAL NUMBER. It would be so so so much appreciated if you could work these out and showed me how you got the answer so I could do it for my course. Thanks and Regards Paris

• Answer:

  too many 1. (2x–1)(x² + 5x - 6) / (4x² – 1)(x – 1) factor where possible x² + 5x – 6 = (x+6)(x–1) 4x² – 1 = (2x+1)(2x–1) now the expression is (2x–1)(x+6)(x–1) / (2x+1)(2x–1)(x – 1) now cancel terms where possible (x+6) / (2x+1) 2. x - 3 / x ÷ x² - 9 / 2x too ambiguous, what is divided by what. First guess x - (3 / x) ÷ x² - (9 / 2)x but there are dozens of other possibilities. #5 thru 8 are similar and cannot be done as is. 3.√3 - √9 - √27 + √81 √3 – (±3) – (±3√3) + (±9) obviously this has many values. Taking just the positive roots, this is √3 – (3) – (3√3) + (9) –2√3 + 6 4. (3+ √3)(1 - 1/ √3) assuming this is (3+ √3)(1 – (1/√3)) multiply 3 – (3/√3) + √3 – 1 2 – (3/√3) + √3 3/√3 can be written as (3/√3) x (√3/√3) = (3√3)/(±3) = ±√3 again, only considering the + root 2 – (√3) + √3 2