Reduce the rational expression to lowest terms. If it is already in lowest terms, enter the expression in the answer box. Also, specify any restrictions on the variable.
25x^2−30x+8/25x^2−16
Before you reduce top and bottom you need to state your restriction on the denominator.
The denominator reads (5x+4)(5x-4) when factored. Set each to zero and solve for x then state the restrictions.
Once that is done, then factor the numerator and see if you can reduce with the denominator : )
To reduce a rational expression to its lowest terms, we need to simplify the numerator and denominator as much as possible. In this case, we have the expression:
(25x^2 - 30x + 8) / (25x^2 - 16)
To factorize the numerator and denominator, we can use the factoring techniques. Factoring the numerator, we get:
25x^2 - 30x + 8 = (5x - 2)(5x - 4)
For the denominator, we have a difference of squares pattern:
25x^2 - 16 = (5x)^2 - 4^2 = (5x + 4)(5x - 4)
Now, we can cancel out the common factors in the numerator and denominator:
(5x - 2)(5x - 4) / (5x + 4)(5x - 4)
Notice that the (5x - 4) terms cancel out. Therefore, the reduced expression is:
(5x - 2) / (5x + 4)
The restriction on the variable is that x cannot equal 4 or -4, since those values would make the denominator zero.