Resolver A=frac{1+a^{2}x^{2}-a^2-x^2}{(1+ax)^2-(x+a)^2}=

$$A = \frac { 1 + a ^ { 2 } x ^ { 2 } - a ^ { 2 } - x ^ { 2 } } { ( 1 + a x ) ^ { 2 } - ( x + a ) ^ { 2 } } =$$

Resolver A (complex solution)

$$A=1$$

$$x\neq -1\text{ and }x\neq 1\text{ and }a\neq -1\text{ and }a\neq 1$$

Pasos para resolver unha ecuación lineal

Usar teorema binomial \left(p+q\right)^{2}=p^{2}+2pq+q^{2} para expandir \left(1+ax\right)^{2}.

$$A=\frac{1+a^{2}x^{2}-a^{2}-x^{2}}{1+2ax+a^{2}x^{2}-\left(x+a\right)^{2}}$$

Usar teorema binomial \left(p+q\right)^{2}=p^{2}+2pq+q^{2} para expandir \left(x+a\right)^{2}.

$$A=\frac{1+a^{2}x^{2}-a^{2}-x^{2}}{1+2ax+a^{2}x^{2}-\left(x^{2}+2xa+a^{2}\right)}$$

Factoriza as expresións que aínda non o están en \frac{1+a^{2}x^{2}-a^{2}-x^{2}}{1+2ax+a^{2}x^{2}-\left(x^{2}+2xa+a^{2}\right)}.

$$A=\frac{\left(a-1\right)\left(x-1\right)\left(a+1\right)\left(x+1\right)}{\left(a-1\right)\left(x-1\right)\left(a+1\right)\left(x+1\right)}$$

Anula \left(a-1\right)\left(x-1\right)\left(a+1\right)\left(x+1\right) no numerador e no denominador.

$$A=1$$

Resolver A

$$A=1$$

$$|x|\neq 1\text{ and }|a|\neq 1$$

Pasos para resolver unha ecuación lineal

Usar teorema binomial \left(p+q\right)^{2}=p^{2}+2pq+q^{2} para expandir \left(1+ax\right)^{2}.

$$A=\frac{1+a^{2}x^{2}-a^{2}-x^{2}}{1+2ax+a^{2}x^{2}-\left(x+a\right)^{2}}$$

Usar teorema binomial \left(p+q\right)^{2}=p^{2}+2pq+q^{2} para expandir \left(x+a\right)^{2}.

$$A=\frac{1+a^{2}x^{2}-a^{2}-x^{2}}{1+2ax+a^{2}x^{2}-\left(x^{2}+2xa+a^{2}\right)}$$

Factoriza as expresións que aínda non o están en \frac{1+a^{2}x^{2}-a^{2}-x^{2}}{1+2ax+a^{2}x^{2}-\left(x^{2}+2xa+a^{2}\right)}.

$$A=\frac{\left(a-1\right)\left(x-1\right)\left(a+1\right)\left(x+1\right)}{\left(a-1\right)\left(x-1\right)\left(a+1\right)\left(x+1\right)}$$

Anula \left(a-1\right)\left(x-1\right)\left(a+1\right)\left(x+1\right) no numerador e no denominador.

$$A=1$$

Resolver a (complex solution)

$$a\in \mathrm{C}\setminus 1,-1$$

$$x\neq -1\text{ and }x\neq 1\text{ and }A=1\text{ and }a\neq -1\text{ and }a\neq 1$$

Resolver a

$$a\in \mathrm{R}\setminus -1,1$$

$$A=1\text{ and }|a|\neq 1\text{ and }|x|\neq 1$$