Question

Simplify m4 -1 ÷m2-1

​

Answer 1

Step-by-step explanation:

The given expression is

\frac{m^4-1}{m^2-1}

m

2

−1

m

4

−1

It can be written as

\frac{(m^2)^2-1^2}{m^2-1}

m

2

−1

(m

2

)

2

−1

2

Using algebraic formula:

a^2-b^2=(a-b)(a+b)a

2

−b

2

=(a−b)(a+b)

\frac{(m^2)^2-1^2}{m^2-1}=\frac{(m^2-1)(m^2+1)}{m^2-1}

m

2

−1

(m

2

)

2

−1

2

=

m

2

−1

(m

2

−1)(m

2

+1)

Cancel out the common factor.

\frac{(m^2)^2-1^2}{m^2-1}=(m^2+1)

m

2

−1

(m

2

)

2

−1

2

=(m

2

+1)

Therefore the simplified form of given expression is m^2+1m

2

+1 .

Answer 2

Answer:

$(m {}^{2} ) {}^{2} - (1) {}^{2} \div m {}^{2} - 1 \\ (m {}^{2} - 1)(m {}^{2} + 1) \div m {}^{2} - 1 \\ = m {}^{2} + 1$