Perform the indicated operations and simplify the expression.

For example. you have,

7r-3/r^2-1

This expression could be,

(7r - 3) / (r^2 - 1), or

[(7r - 3) / r^2] - 1,  or

7r - [3 / (r^2 - 1)]

please check the last expression 3r²-21-1.

There seems to be an error in the last expression. Looking at the problem as a whole, it’s an equation, not just an expression to be simplified. An equation means either an identity that needs to be proved, or an equation with a variable that needs to be solved for that variable.

Nevertheless, I can offer some help. The first multiplier on the right-hand side simplifies to (7r-3)/(2r-3)² if we assume that the division stroke (/) implies that the expressions on either side of it are grouped as a single entity. That being the case, the common denominator r²-1 cancels out and 4r²-12r+9 is the perfect square of 2r-3.

The second multiplier numerator factorises: (r+1)(2r-3), so 2r-3 divides into the denominator of the other multiplier, making it (7r-3)/(2r-3). The denominator of the second multiplier looks wrong, and it could be 3r²-2r-1 which factorises: (3r+1)(r-1), or it could be 3r²+2r-1, factorised as (3r-1)(r+1). Note that r+1 is also a factor in the numerator, so it would cancel it out.

The final part of this is the left-hand side 6r². Although the right-hand side can be simplified, it doesn’t make it easy to solve for r, so the question arises: should the equals sign be an operator such as +, -, ×, ÷?

Please check that you have copied the question accurately and asked the right question. You may be able to solve the problem yourself given the partial details above.

by Top Rated User (696k points)