Rational Expression

Q.

Question 62

Solve the following:

$\frac{x}{2}-\frac{1}{4}(x-\frac{1}{3})=\frac{1}{6}(x+1)+\frac{1}{12}$

Q.

By what number should ${\left(\frac{-3}{2}\right)}^{-3}$be divided so that the quotient may be ${\left(\frac{4}{27}\right)}^{-2}$?

Q.

Question 67

Solve the following:

$3x-\frac{x-2}{3}=4-\frac{x-1}{4}$

Q.

The minimum value of $f\left(x\right)=a^{a^x}+a^{1-a^x}$where $a,$ $x\in R$ and $a>0$, is equal to

1. $a+\frac{1}{a}$

2. $a+1$

3. $2a$

4. $2\sqrt{a}$

Q.

Question 81

Solve the following:

The volume of water in a tank is twice of that in the other. If we draw out 25 litres from the first and add it to the other, the volumes of the water in each tank will be the same. Find the volumes of water in each tank.

Q.

Verify whether the following are zeroes of the polynomial, indicated against them: $\mathrm{p}\left(\mathrm{x}\right)={\mathrm{x}}^2,\mathrm{x}=0$

Q.

Verify whether the given statement is true or false:

$-3$ is a zero of $x-3$

1. True
2. False

Q.

How do you simplify $4$ to the power of $\frac{2}{3}$?

Q.

If $2^{1998}–2^{1997}–2^{1996}+2^{1995}=\mathrm{K}{2}^{1995}$, then the value of $K$is

1. $1$

2. $2$

3. $3$

4. $4$

Q.

If $\frac{52}{x}=\sqrt{\frac{169}{289}}$, then $x=68$.

1. True
2. False

Q.

The value of $1^2-2^2+3^2-4^2+....+{11}^2$ is equal to

1. $55$

2. $66$

3. $77$

4. $88$

Q.

Question 2 (v)

Multiply and reduce to lowest form (if possible):
$\frac{1}{3}\times \frac{15}{8}$

Q.

Verify whether $-1$ and $\frac{3}{2}$ are zeros of the polynomial $p\left(x\right)=2x^3-9x^2+x+12$.

Q.

The simplest form of $\frac{(x^3–1)}{(x^2–1)}$ is

1. (x² + 1)/(x+1)

2. (x² + x + 1)

3. (x² + 2x + 1)/(x+1)

4. (x² + x + 1)/(x+1)

Q.

Reduce the fraction $\frac{56}{40}$ into the lowest terms $:$

Q.

Rewrite in simplest rational exponent form $\sqrt{x}\times 4\sqrt{x}$.

Show each step of your process $8955$

Q.

If $x^2+\frac{1}{x^2}=27$, find $x-\frac{1}{x}$.

Q.

Question 58

Solve the following:

8x-7-3x=6x-2x-3

Q. Reduce the following fraction to the lowest term
$\frac{15}{75}$

Q. Solve for
$x:\frac{1}{\left(x-1\right)\left(x-2\right)}+\frac{1}{\left(x-2\right)\left(x-3\right)}+\frac{1}{\left(x-3\right)\left(x-4\right)}=\frac{1}{6}$

Q.

Question 17

State whether the given statements are true (T) or false (F).

4 : 7 = 20 : 35

Q.

Solve: $(x+2)(x+3)+(x-3)(x-2)-2x(x+1)=0$

Q.

Convert the following into fractions in the lowest form: $4.25$

Q.

Convert the following into fractions in the lowest form: $2.75$

Q. Show that $\frac{a+b+c}{a^{-1}{b}^{-1}+b^{-1}{c}^{-1}+c^{-1}{a}^{-1}}=abc$

Q.

Find the product of the rational expressions 2xyz/(x + y) and $x^2$ + $y^2$ + 2xy)/5xz

Q.

Express each of the following in exponential form:

$\frac{-343}{1024}$

Q.

Simplify the rational expression $\frac{a^2-1}{a^4-1}$ into lowest terms

Q.

Simplify: $\sqrt[qr]{\frac{x^q}{x^r}}\times \sqrt[rp]{\frac{x^r}{x^p}}\times \sqrt[pq]{\frac{x^p}{x^q}}$.

Q. Simplify $\frac{x}{x-1}+\frac{1}{x+1}+\frac{2x}{1-x^2}.$

1. 2
2. 0
3. 1
4. None of the above