Solve for x: (1+x+x^2)/(1-x+x^2)=62(1+x)/63(1-x)
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(1+x+x²)/(1-x+x²) = 62(1+x)/63(1-x)
⇒63(1-x)(1+x+x²) = 62(1+x)(1-x+x²)
⇒63[1+x+x²-x-x²-x³] =62 [ 1-x+x² +x-x²+x³]
⇒63[1-x³]= 62[1+x³]
⇒63-63x³ =62 +62x³
⇒63-62 =62x³+63x³
⇒1= 125 x³
125x³ =1
x³ =1/125
x³ =(1/5)³
∴x=1/5
⇒63(1-x)(1+x+x²) = 62(1+x)(1-x+x²)
⇒63[1+x+x²-x-x²-x³] =62 [ 1-x+x² +x-x²+x³]
⇒63[1-x³]= 62[1+x³]
⇒63-63x³ =62 +62x³
⇒63-62 =62x³+63x³
⇒1= 125 x³
125x³ =1
x³ =1/125
x³ =(1/5)³
∴x=1/5
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