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Question

Simplify: $$[9-{14-(19-\overline{14-12})}]-(14-\overline{15+12})$$


Solution

The BODMAS rule can simplify any expression using these steps of solving:

Brackets (parts of a calculation inside brackets always come first).
Orders (numbers involving powers or square roots).
Division
Multiplication
Addition
Subtraction

Now, using BODMAS rule, we solve the given expression $$\left[ 9−\left\{ 14−\left( 19−\overline { 14-12 }  \right)  \right\}  \right] −\left( 14−\overline { 15+12 }  \right)$$ as follows:

$$\left[ 9−\left\{ 14−\left( 19−\overline { 14-12 }  \right)  \right\}  \right] −\left( 14−\overline { 15+12 }  \right) \\  =\left[ 9−\left\{ 14−\left( 19−2 \right)  \right\}  \right] −\left( 14−27 \right) \\ =\left[ 9−\left\{ 14−17 \right\}  \right] −\left( −13 \right)$$
$$=\left[ 9−\left( −3 \right)  \right] +13\\ =\left[ 9+3 \right] +13\\ =12+13\\ =25$$ 

Hence, $$\left[ 9−\left\{ 14−\left( 19−\overline { 14-12 }  \right)  \right\}  \right] −\left( 14−\overline { 15+12 }  \right)=25$$

Mathematics

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