Biểu thức A=x2+3+x2+1−x2cap A equals the fraction with numerator the square root of x end-root and denominator 2 plus 3 end-fraction plus the fraction with numerator the square root of x end-root and denominator 2 plus 1 end-fraction minus the fraction with numerator the square root of x end-root and denominator 2 end-fraction
?=?√2+3+?√2+1−?√2
có thể được rút gọn thành A=x5+x3−x2cap A equals the fraction with numerator the square root of x end-root and denominator 5 end-fraction plus the fraction with numerator the square root of x end-root and denominator 3 end-fraction minus the fraction with numerator the square root of x end-root and denominator 2 end-fraction
?=?√5+?√3−?√2
. Để rút gọn hoàn toàn, ta quy đồng mẫu số chung là 30, ta được A=6x+10x−15x30=x30cap A equals the fraction with numerator 6 the square root of x end-root plus 10 the square root of x end-root minus 15 the square root of x end-root and denominator 30 end-fraction equals the fraction with numerator the square root of x end-root and denominator 30 end-fraction
?=6?√+10?√−15?√30=?√30
.
Các bước rút gọn:
Phân tích biểu thức ban đầu:
 
Biểu thức đã cho là:
A=x2+3+x2+1−x2cap A equals the fraction with numerator the square root of x end-root and denominator 2 plus 3 end-fraction plus the fraction with numerator the square root of x end-root and denominator 2 plus 1 end-fraction minus the fraction with numerator the square root of x end-root and denominator 2 end-fraction
?=?√2+3+?√2+1−?√2
Tính toán mẫu số: 2+3=52 plus 3 equals 5
2+3=5
2+1=32 plus 1 equals 3
2+1=3
 
Vậy, biểu thức trở thành:
A=x5+x3−x2cap A equals the fraction with numerator the square root of x end-root and denominator 5 end-fraction plus the fraction with numerator the square root of x end-root and denominator 3 end-fraction minus the fraction with numerator the square root of x end-root and denominator 2 end-fraction
?=?√5+?√3−?√2
Quy đồng mẫu số:
 
Mẫu số chung của 5, 3 và 2 là 30.
x5=x×65×6=6x30the fraction with numerator the square root of x end-root and denominator 5 end-fraction equals the fraction with numerator the square root of x end-root cross 6 and denominator 5 cross 6 end-fraction equals the fraction with numerator 6 the square root of x end-root and denominator 30 end-fraction
?√5=?√×65×6=6?√30
x3=x×103×10=10x30the fraction with numerator the square root of x end-root and denominator 3 end-fraction equals the fraction with numerator the square root of x end-root cross 10 and denominator 3 cross 10 end-fraction equals the fraction with numerator 10 the square root of x end-root and denominator 30 end-fraction
?√3=?√×103×10=10?√30
x2=x×152×15=15x30the fraction with numerator the square root of x end-root and denominator 2 end-fraction equals the fraction with numerator the square root of x end-root cross 15 and denominator 2 cross 15 end-fraction equals the fraction with numerator 15 the square root of x end-root and denominator 30 end-fraction
?√2=?√×152×15=15?√30
 
Thực hiện phép cộng và trừ:
 
A=6x30+10x30−15x30cap A equals the fraction with numerator 6 the square root of x end-root and denominator 30 end-fraction plus the fraction with numerator 10 the square root of x end-root and denominator 30 end-fraction minus the fraction with numerator 15 the square root of x end-root and denominator 30 end-fraction
?=6?√30+10?√30−15?√30

A=6x+10x−15x30cap A equals the fraction with numerator 6 the square root of x end-root plus 10 the square root of x end-root minus 15 the square root of x end-root and denominator 30 end-fraction
?=6?√+10?√−15?√30

A=(6+10−15)x30cap A equals the fraction with numerator open paren 6 plus 10 minus 15 close paren the square root of x end-root and denominator 30 end-fraction
?=(6+10−15)?√30

A=(16−15)x30cap A equals the fraction with numerator open paren 16 minus 15 close paren the square root of x end-root and denominator 30 end-fraction
?=(16−15)?√30