the root for ((x^2)-4x+3)/(5(x^2)-18x+9) / ((4x-6)/(10x-6)) is ?
-
x=1
-
((x^(2))-4x+3)/(5(x^(2))-18x+9)/(((4x-6)…
Remove the parentheses around the expression x^(2).
(((x^(2)-4x+3)/(5(x^(2))-18x+9)))/(((4x…
/(10x-6)))
Multiply 5 by each term inside the parentheses.
(((x^(2)-4x+3)/(5x^(2)-18x+9)))/(((4x-6
/(10x-6)))
For a polynomial of the form x^(2)+bx+c, find two factors of c (3) that add up to b (-4). In this problem -1*-3=3 and -1-3=-4, so insert -1 as the right hand term of one factor and -3 as the right-hand term of the other factor.
((((x-1)(x-3))/(5x^(2)-18x+9)))/(((4x-6…
Find the factors such that the product of the factors is the trinomial 5x^(2)-18x+9. This can be done by trial and error and checked using the FOIL method of simplifying polynomials.
((((x-1)(x-3))/((5x-3)(x-3))))/(((4x-6)…
Reduce the expression by canceling out the common factor of (x-3) from the numerator and denominator.
((((x-1)(x-3))/((5x-3)(x-3)…
Reduce the expression by canceling out the common factor of (x-3) from the numerator and denominator.
(((x-1)/(5x-3)))/(((4x-6)/(10x-6)))
Factor out the GCF of 2 from each term in the polynomial.
(2(5x)+2(-3))/(4x-6)*(x-1)/(5x-3)
Factor out the GCF of 2 from 10x-6.
(2(5x-3))/(4x-6)*(x-1)/(5x-3)
Factor out the GCF of 2 from each term in the polynomial.
(2(5x-3))/(2(2x)+2(-3))*(x-1)/(5x-3)
Factor out the GCF of 2 from 4x-6.
(2(5x-3))/(2(2x-3))*(x-1)/(5x-3)
Reduce the expression (2(5x-3))/(2(2x-3)) by removing a factor of 2 from the numerator and denominator.
(5x-3)/(2x-3)*(x-1)/(5x-3)
Reduce the expression by canceling out the common factor of (5x-3) from the numerator and denominator.
((5x-3)(x-1))/((2x-3)(5x-3)…
Reduce the expression by canceling out the common factor of (5x-3) from the numerator and denominator.
(x-1)/(2x-3)
Remove the parentheses around the expression x^(2).
(((x^(2)-4x+3)/(5(x^(2))-18x+9)))/(((4x…
/(10x-6)))
Multiply 5 by each term inside the parentheses.
(((x^(2)-4x+3)/(5x^(2)-18x+9)))/(((4x-6
/(10x-6)))
For a polynomial of the form x^(2)+bx+c, find two factors of c (3) that add up to b (-4). In this problem -1*-3=3 and -1-3=-4, so insert -1 as the right hand term of one factor and -3 as the right-hand term of the other factor.
((((x-1)(x-3))/(5x^(2)-18x+9)))/(((4x-6…
Find the factors such that the product of the factors is the trinomial 5x^(2)-18x+9. This can be done by trial and error and checked using the FOIL method of simplifying polynomials.
((((x-1)(x-3))/((5x-3)(x-3))))/(((4x-6)…
Reduce the expression by canceling out the common factor of (x-3) from the numerator and denominator.
((((x-1)
Reduce the expression by canceling out the common factor of (x-3) from the numerator and denominator.
(((x-1)/(5x-3)))/(((4x-6)/(10x-6)))
Factor out the GCF of 2 from each term in the polynomial.
(2(5x)+2(-3))/(4x-6)*(x-1)/(5x-3)
Factor out the GCF of 2 from 10x-6.
(2(5x-3))/(4x-6)*(x-1)/(5x-3)
Factor out the GCF of 2 from each term in the polynomial.
(2(5x-3))/(2(2x)+2(-3))*(x-1)/(5x-3)
Factor out the GCF of 2 from 4x-6.
(2(5x-3))/(2(2x-3))*(x-1)/(5x-3)
Reduce the expression (2(5x-3))/(2(2x-3)) by removing a factor of 2 from the numerator and denominator.
(5x-3)/(2x-3)*(x-1)/(5x-3)
Reduce the expression by canceling out the common factor of (5x-3) from the numerator and denominator.
(
Reduce the expression by canceling out the common factor of (5x-3) from the numerator and denominator.
(x-1)/(2x-3)
-
Main numerator components:
x^2 - 4x + 3
(x - 3)(x - 1)
5x^2 - 18x + 9
(5x- 3)(x - 3)
[(x - 3)(x - 1)] / [(5x - 3)(x - 3)]
the (x - 3) terms will cancel each other out
you are left with (x - 1) / (5x - 3) in the main numerator <====
Main denominator
(4x - 6) / (10x - 6)
2(2x - 3) / 2(5x - 3)
the 2's will cancel each other out
you are left with (2x - 3) / (5x - 3) in the main denominator <====
Combine the main numerator and the main denominator:
[(x - 1) / (5x - 3)] / [(2x - 3) / (5x - 3)]
invert the main denominator (the fraction) and multiply (rule of dividing by fractions)
[(x - 1) / (5x - 3)][(5x - 3) / (2x - 3)
the terms (5x - 3) will cancel each other out
and you are left with
(x - 1) / (2x - 3) <====
x^2 - 4x + 3
(x - 3)(x - 1)
5x^2 - 18x + 9
(5x- 3)(x - 3)
[(x - 3)(x - 1)] / [(5x - 3)(x - 3)]
the (x - 3) terms will cancel each other out
you are left with (x - 1) / (5x - 3) in the main numerator <====
Main denominator
(4x - 6) / (10x - 6)
2(2x - 3) / 2(5x - 3)
the 2's will cancel each other out
you are left with (2x - 3) / (5x - 3) in the main denominator <====
Combine the main numerator and the main denominator:
[(x - 1) / (5x - 3)] / [(2x - 3) / (5x - 3)]
invert the main denominator (the fraction) and multiply (rule of dividing by fractions)
[(x - 1) / (5x - 3)][(5x - 3) / (2x - 3)
the terms (5x - 3) will cancel each other out
and you are left with
(x - 1) / (2x - 3) <====