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# Simplifying Rational Expressions (Grades 11-12)

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## Simplifying Rational Expressions

1.
To simplify the rational expression $(x+6)/(x^2+5x-6$, what is the factored form of the trinomial in the denominator?
1. $(x+6)(x-1)$
2. $(x-6)(x+1)$
3. $(x-6)(x-1)$
4. $(x+6)(x+1)$
2.
Find the value that makes the rational expression undefined.

$8/(y+6)$
1. $y= -4$
2. $y=0$
3. $y=3$
4. $y=-6$
3.
Find the values that make the rational expression undefined.

$(x^2+3)/(x(x+5)$
1. $x=0$ or $-5$
2. $x=0$ or $7$
3. $x=0$ or $5$
4. $x=2$ or $4$
4.
Simplify the expression $(x-7)/(x^2-x-42)$.
1. $1/(x+7), \ x!=-6$
2. $1/(x+6), \ x!= 7$
3. $x+7, \ x!= -6, 7$
4. $x+6, \ x!= -6, 7$
5.
Simplify. $(x - y)/(x^2 - 2xy + y^2)$
1. $x + y$
2. $xy$
3. $1/(x-y)$
4. $x - y$
6.
Simplify. $(a - 1)/[(a)^2-1]$
1. $1/a, \ a!=0$
2. $1/(a - 1), \ a!= -1$
3. $1/(1- a), \ a!=1$
4. $1/(a + 1), \ a!=1$
7.
Simplify the expression $(7x^2-63)/(x+3)$.
1. $(x+3)/7, \ x!=-3$
2. $(7x^2-9)/(x), \ x!=-3$
3. $7(x+3), \ x!=-3$
4. $7(x-3), \ x!=-3$
8.
Simplify. $(5x + 7y)/( 3(x + y))$
1. $3$
2. $28/3$
3. $-1$
4. No further simplification
9.
Simplify. $(x^2y-x^5y^7+x^8y^4)/(x^2y)$
1. $1-x^3y^6+x^6y^3, \ \ \ \ x,y!=0$
2. $x^4y^2-x^7y^8+x^10y^5, \ \ \ \ x,y!=0$
3. $x^6y^3-x^3y^6-1, \ \ \ \ x,y!=0$
4. $xy-x^3y^6+x^6y^3, \ \ \ \ x,y!=0$
10.
Simplify. $((x^2-y^2)/(y^2-49))/((y-x)/(y+7))$
1. $(y-x)/(y-7), \ x!=y, y!=-7$
2. $(-x+y)/(y-7), \ x!=y, y!= -7$
3. $(-x-y)/(-y-7), \ x!=y, y!=7$
4. $(-x-y)/(y-7), \ x!=y, y!=-7$
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