Question

guys plz answer this question i need help plz​

Answer 1

Solution.

$\mathsf{Now,\:\dfrac{1+x}{1-x}-\dfrac{1-x}{1+x}+\dfrac{4x}{1+x^{2}}+\dfrac{8x^{3}}{1-x^{4}}}$

$\mathsf{=\dfrac{(1+x)^{2}-(1-x)^{2}}{(1-x)(1+x)}+\dfrac{4x}{1+x^{2}}+\dfrac{8x^{3}}{1-x^{4}}}$

$\mathsf{=\dfrac{4x}{1-x^{2}}+\dfrac{4x}{1+x^{2}}+\dfrac{8x^{3}}{1-x^{4}}}$

$\mathsf{=\dfrac{4x(1+x^{2}+1-x^{2})}{(1-x^{2})(1+x^{2})}+\dfrac{8x^{3}}{1-x^{4}}}$

$\mathsf{=\dfrac{4x\times 2}{1-x^{4}}+\dfrac{8x^{3}}{1-x^{4}}}$

$\mathsf{=\dfrac{8x}{1-x^{4}}+\dfrac{8x^{3}}{1-x^{4}}}$

$\mathsf{=\dfrac{8x}{1-x^{4}}(1+x^{2})}$

$\mathsf{=\dfrac{8x}{(1+x^{2})(1-x^{2})}(1+x^{2})}$

$\mathsf{=\dfrac{8x}{1-x^{2}}}$

Remember.

• $\mathsf{(a+b)^{2}-(a-b)^{2}=4ab}$

• $\mathsf{(a+b)(a-b)=a^{2}-b^{2}}$