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nameVoid
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i can take this down to
How Do You Simplify Complex Algebraic Expressions?
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In summary, we are trying to simplify the expression {(\sqrt{a} + 1)^2 - {a-\sqrt {ax} \over \sqrt a - \sqrt x} \over (\sqrt a + 1)^3 - a \sqrt a + 2}. We can simplify it to {1 \over 3} by grouping like terms and canceling out some terms.
i can take this down to
- #2
whybother
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So you are trying to simplify the expression, I take it?
[tex]{(\sqrt{a} + 1)^2 - {a-\sqrt {ax} \over \sqrt a - \sqrt x} \over (\sqrt a + 1)^3 - a \sqrt a + 2} [/tex]
= [tex]{(a + 2 \sqrt a + 1)(\sqrt a - \sqrt x) - (a - \sqrt {ax}) \over (\sqrt a - \sqrt x)((\sqrt a + 1)^3 - a \sqrt a + 2)} [/tex]
= [tex]{a \sqrt a - a \sqrt x +2a - 2 \sqrt a \sqrt x + \sqrt a - \sqrt x - a + \sqrt{ax} \over (\sqrt a - \sqrt x)(a^{3 \over 2} + 3a + 3 \sqrt a + 1 - a^{3 \over 2} + 2)} [/tex]
And then we group like terms and can cancel some things out
=[tex] {a \sqrt a + a + \sqrt a - a \sqrt x - \sqrt{ax} - \sqrt x \over 3(a \sqrt a + a + \sqrt a - a \sqrt x - \sqrt a \sqrt x - \sqrt x} [/tex]
= [tex] {1 \over 3} [/tex]
[tex]{(\sqrt{a} + 1)^2 - {a-\sqrt {ax} \over \sqrt a - \sqrt x} \over (\sqrt a + 1)^3 - a \sqrt a + 2} [/tex]
= [tex]{(a + 2 \sqrt a + 1)(\sqrt a - \sqrt x) - (a - \sqrt {ax}) \over (\sqrt a - \sqrt x)((\sqrt a + 1)^3 - a \sqrt a + 2)} [/tex]
= [tex]{a \sqrt a - a \sqrt x +2a - 2 \sqrt a \sqrt x + \sqrt a - \sqrt x - a + \sqrt{ax} \over (\sqrt a - \sqrt x)(a^{3 \over 2} + 3a + 3 \sqrt a + 1 - a^{3 \over 2} + 2)} [/tex]
And then we group like terms and can cancel some things out
=[tex] {a \sqrt a + a + \sqrt a - a \sqrt x - \sqrt{ax} - \sqrt x \over 3(a \sqrt a + a + \sqrt a - a \sqrt x - \sqrt a \sqrt x - \sqrt x} [/tex]
= [tex] {1 \over 3} [/tex]
FAQ: How Do You Simplify Complex Algebraic Expressions?
1. What is an algebraic expression?
An algebraic expression is a mathematical phrase that uses numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. It does not contain an equal sign and cannot be solved as it is.
2. How is an algebraic expression different from an algebraic equation?
An algebraic expression does not have an equal sign and cannot be solved, while an algebraic equation has an equal sign and can be solved to find the value of the variable.
3. What are the key components of an algebraic expression?
The key components of an algebraic expression are variables, constants, and mathematical operations. Variables are represented by letters and can take on different values, while constants are fixed values. The mathematical operations determine how the variables and constants are related.
4. How can algebraic expressions be simplified?
Algebraic expressions can be simplified by combining like terms, grouping like terms, and using the distributive property. This involves combining numbers with the same variables and exponents, and applying the appropriate mathematical operations.
5. What are some real-life applications of algebraic expressions?
Algebraic expressions are used in many real-life situations, such as calculating the total cost of a shopping trip including tax, determining the amount of interest on a loan, and finding the area of a shape with variable dimensions. They are also used in science and engineering for solving complex equations and modeling real-world problems.