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\left(99\times 99+1\right)x-\left(99\times 99+1\right)=0
Multiply both sides of the equation by 99.
\left(9801+1\right)x-\left(99\times 99+1\right)=0
Multiply 99 and 99 to get 9801.
9802x-\left(99\times 99+1\right)=0
Add 9801 and 1 to get 9802.
9802x-\left(9801+1\right)=0
Multiply 99 and 99 to get 9801.
9802x-9802=0
Add 9801 and 1 to get 9802.
9802x=9802
Add 9802 to both sides. Anything plus zero gives itself.
x=\frac{9802}{9802}
Divide both sides by 9802.
x=1
Divide 9802 by 9802 to get 1.