Respuestas
x+1
2
=
x−1
1
2 Multiplica en cruz.
2(x-1)=x+12(x−1)=x+1
3 Expandir.
2x-2=x+12x−2=x+1
4 Suma 22 a ambos lados.
2x=x+1+22x=x+1+2
5 Simplifica x+1+2x+1+2 a x+3x+3.
2x=x+32x=x+3
6 Resta xx en ambos lados.
2x-x=32x−x=3
7 Simplifica 2x-x2x−x a xx.
x=3x=3
8 También ten en cuenta que xx no está definida en -1,1−1,1.
\begin{aligned}&x\ne -1\\&x\ne 1\end{aligned}
x≠−1
x≠1
9 A partir de los valores de xx, tenemos estos 4 intervalos para probar.
\begin{aligned}&x<-1\\&-1<x<1\\&1<x<3\\&x>3\end{aligned}
x<−1
−1<x<1
1<x<3
x>3
10 Elige un punto de prueba para cada intervalo.
For the interval x<-1x<−1:
Let's pick x=-2x=−2. Then, \frac{2}{-2+1}>\frac{1}{-2-1}
−2+1
2
>
−2−1
1
.
After simplifying, we get -2>-0.333333−2>−0.333333, which is false.
Descarta este intervalo..
For the interval -1<x<1−1<x<1:
Let's pick x=0x=0. Then, \frac{2}{0+1}>\frac{1}{0-1}
0+1
2
>
0−1
1
.
After simplifying, we get 2>-12>−1, which is true.
Mantén este intervalo..
For the interval 1<x<31<x<3:
Let's pick x=2x=2. Then, \frac{2}{2+1}>\frac{1}{2-1}
2+1
2
>
2−1
1
.
After simplifying, we get 0.666667>10.666667>1, which is false.
Descarta este intervalo..
For the interval x>3x>3:
Let's pick x=4x=4. Then, \frac{2}{4+1}>\frac{1}{4-1}
4+1
2
>
4−1
1
.
After simplifying, we get 0.4>0.3333330.4>0.333333, which is true.
Mantén este intervalo..
11 Por lo tanto,
\begin{aligned}&-1<x<1\\&x>3\end{aligned}
−1<x<1
x>3
entra a cymath