smc-4356-12-Subtraction

JACK v1 Functions, 2ADV F1 2008 HSC 1c

Simplify `2/n-1/(n+1)`. (2 marks)

--- 4 WORK AREA LINES (style=lined) ---

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`(n + 2)/(n(n+1))`

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`2/n-1/(n+1)`

`= (2(n+1)-1(n))/(n(n+1))`

`= (2n + 2-n)/(n(n+1))`

`= (n+2)/(n(n+1))`

Algebraic Techniques, SMB-069

Factorise the expression `5/(x^2-1)-3/(x-1)` (3 marks)

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`(2-3x)/((x-1)(x+1))`

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`5/(x^2-1)-3/(x-1)`	`=5/((x+1)(x-1))-3/(x-1)`
	`=5/((x+1)(x-1))-(3(x+1))/((x+1)(x-1))`
	`=(5-3(x+1))/((x-1)(x+1))`
	`=(2-3x)/((x-1)(x+1))`

Algebraic Techniques, SMB-068

Factorise the expression `5/(b^2-b)-2/(b^2-1)` (3 marks)

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`(3b+5)/(b(b-1)(b+1))`

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`5/(b^2-b)-2/(b^2-1)`	`=5/(b(b-1))-2/((b+1)(b-1))`
	`=(5(b+1))/(b(b-1)(b+1))-(2b)/(b(b-1)(b+1))`
	`=(5b+5-2b)/(b(b-1)(b+1))`
	`=(3b+5)/(b(b-1)(b+1))`

Algebraic Techniques, SMB-053

Simplify the expression `(4y+1)/8-(6-2y)/3` (2 marks)

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`(28y-45)/24`

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`(4y+1)/8-(6-2y)/3`	`=(3(4y+1))/24-(8(6-2y))/24`
	`=(12y+3-48+16y)/24`
	`=(28y-45)/24`

Algebraic Techniques, SMB-052

Simplify the expression `(3a+2)/3-(2a-1)/5` (2 marks)

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`(9a+13)/15`

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`(3a+2)/3-(2a-1)/5`	`=(5(3a+2))/15-(3(2a-1))/15`
	`=(15a+10-6a+3)/15`
	`=(9a+13)/15`

Algebraic Techniques, SMB-051

Simplify the expression `x/4-(x+2)/5` (2 marks)

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`(x-8)/20`

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`x/4-(x+2)/5`	`=(5x)/20-(4(x+2))/20`
	`=(5x-4x-8)/20`
	`=(x-8)/20`

Algebraic Techniques, SMB-035

Simplify the expression `5/(4a)-1/(3a)` (2 marks)

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`11/(12a)`

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`5/(4a)-1/(3a)`	`=(5xx3)/(12a)-(1xx4)/(12a)`
	`=(15-4)/(12a)`
	`=11/(12a)`

Algebraic Techniques, SMB-034

Simplify the expression `3/x-1/(2x)` (2 marks)

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`5/(2x)`

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`3/x-1/(2x)`	`=6/(2x)-1/(2x)`
	`=(6-1)/(2x)`
	`=5/(2x)`

Algebraic Techniques, SMB-006

Simplify the expression `(5x)/9-x/6` (2 marks)

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`(7x)/18`

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`(5x)/9-x/6`	`=(10x)/18-(3x)/18`
	`=(7x)/18`

Algebraic Techniques, SMB-505

Simplify the expression `b/2-b/3` (2 marks)

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`b/6`

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`b/2-b/3`	`=(3b)/6-(2b)/6`
	`=b/6`

Algebraic Techniques, SMB-005

Simplify the expression `(4x)/5-(x)/3` (2 marks)

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`(7x)/15`

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`(4x)/5-(x)/3`	`=(12x)/15-(5x)/15`
	`=(7x)/15`

Algebraic Techniques, SMB-004

Simplify the expression `(3t)/5-(t)/2` (2 marks)

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`(t)/10`

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`(3t)/5-(t)/2`	`=(6t)/10-(5t)/10`
	`=(t)/10`

Functions, 2ADV F1 2008 HSC 1c

Simplify `2/n-1/(n+1)`. (2 marks)

--- 4 WORK AREA LINES (style=lined) ---

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`(n + 2)/(n(n+1))`

Show Worked Solution

`2/n-1/(n+1)`

`= (2(n+1)-1(n))/(n(n+1))`

`= (2n + 2-n)/(n(n+1))`

`= (n+2)/(n(n+1))`