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anemone
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Simplify the expression $\dfrac{\sqrt{1+\sqrt{1-a^2}}((1+a)\sqrt{1+a}-(1-a)\sqrt{1-a})}{a(2+\sqrt{1-a^2})}$.
Albert said:$\sqrt 2$
Is it correct ?
anemone said:Simplify the expression $\dfrac{\sqrt{1+\sqrt{1-a^2}}((1+a)\sqrt{1+a}-(1-a)\sqrt{1-a})}{a(2+\sqrt{1-a^2})}---(1)$.
Simplifying expressions is a way to rewrite complex mathematical expressions in a simpler and more concise form. This makes it easier to solve equations and perform other mathematical operations.
To simplify an expression, you must combine like terms, use the distributive property, and apply basic mathematical operations such as addition, subtraction, multiplication, and division. It is also important to follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).
Not all expressions can be simplified, as it depends on the complexity of the expression and the given variables. Some expressions may already be in their simplest form and cannot be further simplified.
Simplifying expressions can make mathematical equations easier to understand and solve. It also helps in identifying patterns and relationships between different terms in the expression.
In real-life situations, simplifying expressions can help in making calculations and measurements more efficient and accurate. It can also be applied in various fields such as finance, physics, and engineering to solve complex problems and make predictions.