Year 11 revision (1 Viewer)

[Makro]

For my half yearlies, just doing the chapter reviews for a few questions.

Simplify: 3/(x-2) + 1/(x+3) - 2/(x^2 + x - 6)

Simplify with a rational denominator:

3/({sqrt}5) + 2) - {sqrt}2/(2{sqrt}2 - 1)

Solve simultaneously:

x - y + 7 = 0
3x - 4y + 26 = 0

Sorry doesn't let me use LATEX for beginning a topic :/ All help appreciated.

 

[Makro]

I couldn't get the simultaneous one with elimination method, but I just got it with sub.

 

[vds700]

Simplify: 3/(x-2) + 1/(x+3) - 2/(x^2 + x - 6)

=3/(x - 2) + 1/(x + 3) - 2/[(x + 3)(x - 2)]
=3(x + 3)/[(x + 3)(x - 2)] + (x - 2)/[(x + 3)(x - 2)] - 2/[(x + 3)(x - 2)]
=[3(x + 3) + (x - 2) - 2]/[(x + 3)(x - 2)]
=(4x + 5)/[(x + 3)(x - 2)]

Simplify with a rational denominator:

3/({sqrt}5) + 2) - {sqrt}2/(2{sqrt}2 - 1)

3/(sqrt5 + 2)
= 3(sqrt5-2)/(sqrt5+2)(sqrt5-2)
=(3sqrt5 - 6)/(5-4)
=3sqrt5-6

sqrt2/(2sqrt2-1)
=sqrt2(2sqrt2+1)/[(2sqrt2-1)(2sqrt2+1)]
=(4 + sqrt2)/(8-1)
=4/7 + (sqrt2)/7

now 3/({sqrt}5) + 2) - {sqrt}2/(2{sqrt}2 - 1) = 3sqrt5-6 - 4/7 - (sqrt2)/7
=[sqrt5- (sqrt2)/7] - 46/7

Solve simultaneously:

x - y + 7 = 0
3x - 4y + 26 = 0

Sorry doesn't let me use LATEX for beginning a topic :/ All help appreciated.[/quote]

 

[kurt.physics]

Solve simultaneously:

x - y + 7 = 0
3x - 4y + 26 = 0

-------------------------

 

[Makro]

Thanks!