Simplification of Rational Algebraic Expression

Q. Factorise the expressions and divide them as directed.
$(y^2+7y+10)÷(y+5)$
[3 marks]

Q.

The value of $\frac{x(x+1)(x+2)(x+3)}{x(x+1)}$ is __________.

1. (x+3)

2. x(x+1)

3. (x + 2) (x + 3)

4. (x+2)

Q. ($p^3{q}^6-p^6{q}^3)÷p^3{q}^3$ = _________.

1. $p^3-q^3$
2. $p^3+q^3$
3. $q^3-p^3$
4. $-p^3-q^3$

Q. $10y(6y+21)÷5(2y+7)$ = _________.

1. $10y$
2. $6y$
3. $(2y+7)$
4. $(6y+21)$

Q.

State whether true or false:
$\frac{(3x^2+1)}{\left(3x^2\right)}=1+1=2$

1. True

2. False

Q.

Find the value of the given expression
$(x^3+2x^2+3x)÷2x$

1. 1/2(x²+2x+3)

2. 1/2

3. (x²+2x+3)

4. 1

Q.

On dividing $\left(24x{y}^2\right)\left(z^2\right)$ by $6y{z}^2$, we get

1. 4xy

2. 4yz

3. 4xyz

4. 4xz

Q. The simplified form of $\frac{x^2-9y^2}{x^3-27y^3}$ is _______.

1. $\frac{x+3y}{x^2+3xy+9y^2}$
2. $\frac{x^2+3xy+9y^2}{x+3y}$
3. $\frac{x^2+6xy+9y^2}{x+3y}$
4. $x+3y$

Q.

Which of the following is the expression obtained by the division of $5pq(p^2-q^2)$ by $2p(p+q)?$

1. $\frac{5q(p-q)}{2}$

2. $\frac{5q(p+q)}{4}$

3. $\frac{5q(p-q)}{4}$

4. $\frac{5q(p+q)}{2}$

Q. $(x^3+2x^2+3x)÷2x$ = ___________.

1. $x^2+2x+3$
2. $2x^2+2x+3$
3. $2x^2+2x+6$
4. $\frac{1}{2}(x^2+2x+3)$