1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
madam [21]
3 years ago
8

Solve the equation x+3/x-4 = x-5/x+4

Mathematics
1 answer:
Serga [27]3 years ago
7 0

Answer:

\large\boxed{x=\dfrac{1}{2}}

Step-by-step explanation:

\dfrac{x+3}{x-4}=\dfrac{x-5}{x+4}\\\\\text{Domain:}\ x-4\neq0\ \wedge\ x+4\neq0\\\\x\neq4\ \wedge\ x\neq-4\\\\D:x\in\mathbb{R}-\{-4,\ 4\}

\dfrac{x+3}{x-4}=\dfrac{x-5}{x+4}\qquad\text{cross multiply}\\\\(x+3)(x+4)=(x-4)(x-5)\qquad\text{use FOIL}\ (a+b)(c+d)=ac+ad+bc+bd\\\\(x)(x)+(x)(4)+(3)(x)+(3)(4)=(x)(x)+(x)(-5)+(-4)(x)+(-4)(-5)\\\\x^2+4x+3x+12=x^2-5x-4x+20\qquad\text{combine like terms}\\\\x^2+(4x+3x)+12=x^2+(-5x-4x)+20\\\\x^2+7x+12=x^2-9x+20\qquad\text{subtract}\ x^2\ \text{from both sides}\\\\7x+12=-9x+20\qquad\text{subtract 12 from both sides}\\\\7x=-9x+8\qquad\text{add}\ 9x\ \text{to both sides}\\\\16x=8\qquad\text{divide both sides by 16}\\\\x=\dfrac{8}{16}\\\\x=\dfrac{8:8}{16:8}\\\\x=\dfrac{1}{2}\in D

You might be interested in
Solve <img src="https://tex.z-dn.net/?f=6x%5E%7B2%7D%20-42%3D0" id="TexFormula1" title="6x^{2} -42=0" alt="6x^{2} -42=0" align="
Citrus2011 [14]

6x^2-42=0\implies 6x^2=42\implies x^2=\cfrac{42}{6}\implies x^2=7 \\\\\\ x=\pm\sqrt{7}\implies x\approx \pm 2.65

8 0
2 years ago
How is the interquartile range calculated?
Nastasia [14]
It is the difference between the third and the first quartile
3 0
3 years ago
Read 2 more answers
Write the point-slope form of the equation of the line that passes through the points (6, 6) and (-6, 1). Include your work in y
Allushta [10]

Answer:

Step-by-step explanation:

you need the formula (y-y1) = m(x-x1) that uses a slope and a point

m=(y1-y2)/(x2-x1)= 6-1/6+6=5/12

now pic any poit out of the 2 given ones

Answer:

(y-6) =(5/12)(x-6)

same for all the other

3 0
3 years ago
100 points. Fun question to do.
Ganezh [65]

Answer:

Step-by-step explanation:

1.Wound wash

2.It helps wounds

3a.to the materals

3b.to tell whats in the product.

5 0
3 years ago
Read 2 more answers
A zoo had 2250 visitors on Friday and 4725 on Saturday. What was the percent of increase of the number of visitors on Saturday o
NARA [144]
4725-2250= 2475
2475/2250 x100= 110
It increased by 110%
7 0
3 years ago
Other questions:
  • What is 520% written as a fraction
    13·1 answer
  • There are fewer rational numbers than irrational numbers. A. True B. False
    7·2 answers
  • (Class 11 Trigonometry)<br>step by step explanation needed​<br>(will mark brainliest if it helps me)
    7·1 answer
  • A principle of $12000 was invested into 2 accounts. One account was invested in muni bonds which generated 6% interest rate. The
    6·1 answer
  • Jake volunteers to help out his younger brother's basketball team in his free time. One of his tasks is to ensure that all the b
    9·2 answers
  • Here is a diagram of a person standing next to a tree.
    13·2 answers
  • A city has a population of 350,000. The population has decreased by 30% in the past ten years. What was the population of the ci
    14·1 answer
  • Kendrea is 4 times 2 less than Cameron's age. Kendrea is 40 years old. How
    11·1 answer
  • If f(x)f(x) is an exponential function where f(3.5)=12f(3.5)=12 and f(9)=75f(9)=75, then find the value of f(7.5)f(7.5), to the
    8·1 answer
  • If 2/3x − 1 = 4, then x=
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!