Simplify (^{3}/_{4} + ^{1}/_{3}) x 4^{1}/_{3} + 3^{1}/_{4}

Answer Details

To simplify this expression, we need to follow the order of operations, which is Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction (PEMDAS). First, we can simplify the expression inside the parentheses: (^{3}/_{4} + ^{1}/_{3}) x 4^{1}/_{3} + 3^{1}/_{4} = (^{9}/_{12} + ^{4}/_{12}) x 4^{1}/_{3} + 3^{1}/_{4} = ^{13}/_{12} x 4^{1}/_{3} + 3^{1}/_{4} Next, we can simplify the exponent 4^{1}/_{3}. To do this, we can convert the mixed number to an improper fraction: 4^{1}/_{3} = ^{(4 x 3) + 1}/_{3} = ^{13}/_{3} Now we can substitute the value of 4^{1}/_{3} into the expression: ^{13}/_{12} x 4^{1}/_{3} + 3^{1}/_{4} = ^{13}/_{12} x ^{13}/_{3} + ^{13}/_{4} To simplify this, we can first simplify the multiplication of fractions: ^{13}/_{12} x ^{13}/_{3} = ^{169}/_{36} Now we can add the two fractions: ^{169}/_{36} + ^{13}/_{4} = ^{169}/_{36} + ^{39}/_{36} = ^{208}/_{36} = ^{13}{9} Therefore, the simplified expression is ^{13}{9}, which corresponds to option (E).