Consider the expressions $\frac{4x^3+2x^2+6x+7}{2x+1}$ and $2x^2+3+\frac4{2x+1}.$a) Show that these expressions are equal when $x=10.$

b) Explain why these expressions are not equal when $x=-\dfrac12.$

c) Show that these expressions are equal for all $x$ other than $-\dfrac12.$

In parts (a) and (c), begin by explaining what your strategy for solving will be.

Part (a)  We shall simplify both of them in order to find the solution to the equation.

• Once we've done that, we'll see that they have the same equation, so we can match the equation if x=10.

Part (b)  When x=-1/2, the answers to the second expression, 2x2, change to -1, and we eventually arrive in 1.

• This is why the expressions are not equal at this point.

Part (c)  As we can see, the expressions are identical, thus we can demonstrate that they are equal if x is any number other than -1/2.

What is an expression in maths?

• An expression is a set of terms combined using the operations +, – , x or , for example 4 x − 3 or x 2 – x y + 17 .
• An equation states that two expressions are equal in value, for example 4 b − 2 = 6 .
• An identity is a statement that is true no matter what values are chosen, for example 4 a × a 2 = 4 a 3 .

What is a math expression example?

• An expression is a set of numbers or variables combined using the operations +, –, × or ÷.
• Arithmetic expression that contains only numbers and mathematical operators and algebraic expression that contains variables, numbers and mathematical operators.

How do you find expressions?

• To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.
• To evaluate an expression, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations.

Learn more about expressions here:

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Answer:

Part a)  In order to solve the equation, we will simplify both of them.  Once we do that, if we notice, they are the same equation, so therefore, if x=10, then we will be able to match the equation.

Part b) The reason the expressions are not equal when x=-1/2 is because if we see, that in the second expression, 2x^2, if x=-1/2, then the answer becomes -1, and we eventually end up with 1.

Part c)  As we can see, the expressions are the same, so if x is any number other than -1/2, then we will be able to show that the expressions are equal.

Step-by-step explanation:

You can simplify the explanation, also if you play ROBLOX, follow me at my username: BAMUNJI, or 24KBlingYT

By the way, this question is from the Art of Problem Solving, and you should not just copy answers or copy of them.